Marian - Aquila

If you don't have Aquila yet but want to try her out, she is available to try in story chapter 16 "Back from Bygone" ( Main Story // Journey // Ulster )

Aquila is both a capable main dps and a strong support.
As a DPS, Marian can easily deal good single-target damage or AoE damage over a wide area, although she has to wait for her drone to move before she starts dealing good dps, and this can lead to Marian having somewhat weak mobility.
Note that Marian deals entirely skill damage if dealing AoE damage, but mostly ballistic damage when dealing single-target damage, which can make teambuilding very difficult.

As a support, Marian provides strong buffs to the team, whilst also dealing good damage as well, although Aquila constantly dealing damage makes her incompatible with the games best support (Vidya - Celestial Swan) for all dps operatives that don't deal kinetic damage.
Despite that, Aquila is a strong support, and when not alongside Vidya, Aquila is probably the games most general support, able to support literally every dps operative very well.

The Basics

Role: Support - Buffs Damage
(She can support everybody)
Deals Kinetic Damage
Weapon Type: SMG
Deals
AoE: Entirely skill damage
Single-Target: both ballistic+skill
Mobility is average

How to use Marian - Aquila as a Support

Use her Support Skill at the start of a fight.

That's it. She'll just passively boost your ATK and damage.
(Her buff lasts indefinitely provided you just keep dealing damage.)

How to use Marian - Aquila as a DPS

Spam Marian's Ult off-cooldown.

Use Marian's Standard Skill to move her Beacon near the enemy
or
Hold Marian's Standard Skill to have her Beacon follow an enemy

then:
Against Single Targets: Shoot the enemy
Against Groups: Shoot the Beacon
Provided the enemy is within the Beacons PBAoE, she has functionally unlimited ammo, whether she shoots at the enemy or the Beacon.

How to build Marian - Aquila

Weapon: Core Prism / Glorious Laurel
Weapon Parts: Max ATK
Logistics Squad: Truffle
Basic: + 10.0% ATK
+ 106 Alignment Index
Special: +8.5% Kinetic Damage
Best teammates with Aquila as a DPS:
Vidya - Celestial Swan
Siris - Freefin
Marian - Riptide
Best teammates with Aquila as a Support:
Aquila can support all operatives.
(Except Mauxir - Lotus)
She works slightly less well with operatives that base their damage on their own HP instead of their ATK.

Specifics:

Standard Skill

Aquila passively deploys a "Fang Beacon" - a giant floating tech thing that follows Aquila around.
This has a large PBAoE around it, which is easily visible on the groumd.
Use Aquila's Standard Skill to move the Beacon to the targeted location. Hold it to have it follow the targeted enemy. If it gets too far from Marian, it returns automatically.

Whenever Aquila's shots hit either the beacon or an enemy in the beacons PBAoE, Marian gets 1 "Fangfire Energy"

When Aquila has 20 Fangfire Energy, her Beacon does an extra attack:
If you hit an enemy - Deals extra Kinetic damage to the target
If you hit the beacon - Deal AoE Kinetic Damage (to up to 5 targets)
With its Neuronic, the beacon proc'ing also grants Aquila 30 bullets.
Given that it takes 20 bullets to activate, but gives 30 back, Marian can shoot literally indefinitely provided she keeps shooting her Beacon or enemies near it.

Each hit via her Beacon also gives Aquila 1 "Raptor Energy".
When Aquila has 5 (3 with her Neuronic) Raptor Energy, her next does another extra hit:
If you hit an enemy - Deals extra Kinetic damage to the target 6 times
If you hit the beacon - Deal AoE Kinetic Damage 3 times (to up to 5 targets)
Enemies damaged have "Rending Wound" applied to them, which deals 10% Kinetic Damage every 0.5s for 10s (so 200% total).
This counts as "Gashed", and also counts as Standard Skill DMG.

Note that whilst the wording of the skill might imply that the Beacon is an extension of Aquila's damage, and thus the damage dealt by the Beacon is the same [type] as Aquila, this isn't true - Whilst it may be proc'd by Aquila's ballistic damage, the Beacon's damage isn't Aquila's ballistic damage, meaning it doesn't benefit from things like per-shot Aptitude buffs (e.g. from Tess - Phantasia), and instead it counts as Skill Damage, and hence can be used to for example charge Siris - Freefin's Freetide buff.

Ultimate Skill

Aquila deals strong AoE damage in front of her.

This has a pretty short cooldown of 20s, and a relatively low U-Energy cost of 40, meaning it's pretty spammable.
This is good, as its Neuronics provide decent buffs to Aquila's damage for 10s after using her ult.

If using Marian as a dps, you can just spam this as often as you can.

Aquila can't use her ult whilst her support skill is active. I am unsure if this is a bug, but it means that you'll never use Aquila's ult whilst using her as a support, as her support skill is much better than her ult.

Support Skill

Marian enters "Sky Hunt" state, gaining 1 "Raptor's Sight" every 0.1s. (or gaining 2 every 0.1s with its Neuronic)

When Marian has 80 Raptor's Sight, the next time the deployed operative deals damage, Marian consumes all her Raptor's Sight to deal extra damage.
This is a single-target hit to the target, followed by three AoE hits around the target.
This also inflicts Rending Wound (Gashed) for 10s as well.

Whilst in this state, Aquila increases the ATK of the deployed operative, by a percentage of Aquila's own ATK.
Marian also doesn't restore S-Energy, and being in the state continuously consumes S-Energy (2.5/s) while in combat.
You can of course toggle the skill off, but it exits automatically when reaching 0 S-Energy.
At a drain rate of 2.5 S-Energy/s, this has an uptime of 20s. On a 10s cooldown it's default uptime is 66.6%.

The cooldown for this skill starts when Aquila exits the state, at which point she gains 50 S-Energy, allowing her to instantly use the skill again when it comes off cooldown.

With its first Neuronic, Marian gains S-Energy whenever an enemy is damaged, up to once per second.
Since her S-Energy drain rate is only 2.5 S-Energy/second, this Neuronic allows Aquilato gain 5/s means she can have literally infinite uptime on her Support Skill.

Since (with its Neuronic) Aquila gains 2 Raptor's Sight every 0.1s, she'll get to the max of 80 in 4 seconds.

This skill plays like other passive support operatives such as Vidya - Celestial Swan and Siris - Freefin.
Just use Aquila's Support Skill at the start of combat, and it should sustain itself indefinitely, providing passive buffs, provided you keep dealing damage.

Weapon

Core Prism
Her signature 5* weapon.
Gives her more ATK.
Increases the DMG dealt by both Marian and the deployed operative.
After her Support Skill hits, increases the damage the enemy takes for 10s.
As usual for 5* weapons, the "increases damage taken" part is by-far the strongest.
Since that part doesn't apply when using Marian as a main dps, Core Prism is much better at buffing Marian as a support than buffing her as a main dps.
Glorious Laurel
Her signature 4*.
This gives 15% Kinetic damage for both Marian and the deployed operative.
It also increases Marian's Support Skills damage by 30%, which is great.

If you don't have either of those, then:
If using Marian as a DPS: use whatever Kinetic SMG you have that deals the most damage - Marian just wants generic buffs like ATK and damage, nothing special.
If using Marian as a support, then give her Frigatebird - it gives the deployed operative and ATK buff after Aquila uses her Support Skill, which is great.

For weapon parts Marian wants maximum ATK.

Logistics

Squad

Use Truffle squad - it was specifically designed for her, and is her best logistics squad.

Truffle increases Marian and the deployed operatives DMG by 30% when she is off-field using her Support Skill, as well as increasing Marian's damage by 30% when she is on-field.
It also gives another DMG boost to the deployed operative for 8s after Marian deals damage with her Beacon/Support Skill.

Stats

For stats, Marian wants:
Basic: + 10.0% ATK
+ 106 Alignment Index
Special: +8.5% Kinetic Damage

ATK to boost her damage, as well as the ATK buff she provides when being used as a support.
Alignment Index boosts the squads damage to targets affliced with Gashed.
Aquila inflicts this with her Standard Skill's Raptor Energy hits, as well as the hits from her Support Skill.

Other Stats

Since Aquila's Standard Skill has an S-Energy cost of 0, and she automatically recovers all her S-Energy after her Support Skill ends, S-Energy Regen is literally useless to Aquila.
U-Energy Regen is a decent cope stat, as Aquila's ult is pretty good, but it's nowhere near as useful as Alignment Index.
Aquila can't heal or create shields
A lot of Aquila's damage is skill damage, and skills can't crit, so crit mods aren't very useful for Marian.
She also has a lot base Crit DMG value of just 30%, so even in optimal conditions Crit DMG Amplifier mods still aren't that great for her.

Manifestation

M1 causes the enemy to take 4% more damage taken for 8s after Marian deals skill damage to them.
This stacks up to 3 times (12%).
12% increased damage taken is very strong.
With M2, Marian and the deployed operative ignore 12% Resistance whilst Marian is using her Support Skill.
This is also very strong.
With M3, Marian dealing skill damage increases the deployed operative damage by 5% for 8s, up to 4 times (20%).
A decent bonus, but not that strong.
(Also, yes, this can buff Aquila herself or the deployed operative.
M4 gives the usual +1 skill level to Aquila's Support Skill, increasing its ATK buff and damage by 10%.
With M5, Marian using her Support Skill gives the deployed operative a +20% ATK buff.
Just a nice damage buff with no real strings attached.

You should get Aquila to M2, as her first two Manifestations are both very strong.
M3 is a decent bonus that isn't too expensive, making it a cost-efficient place to stop, but it's not that strong.

Good Teammates for Marian - Aquila

Good Teammates for Marian - Aquila as a Support

Aquila provides DMG Dealt buffs that make her a useful support for literally all operatives in the game.
She also provides ATK buffs that are very useful to almost all main dps operatrives too.

Aquila does constantly deal Kinetic damage though, so if using both Aquila and Vidya - Celestial Swan, then you'll need your main DPS to deal Kinetic Damage.
This limits Aquila + Vidya to only being usable for kinetic-damage operatives, but they are a fantastic pair of supports for all kinetic-damage operatives.

When not paired with Vidya though, Aquila works well as a support for all operatives, and she is probably one of the games most generic supports (again though, only when not alongside Vidya).

Note that since Mauxir - Lotus doesn't deal damage herself (all her damage comes from her summoned Nodes/Drones), Aquila is basically useless as a support for Lotus.

Good Teammates for Marian - Aquila as a DPS

Aquila's Beacon deals skill damage, whereas Aquila herself deals ballistic damage.

Against groups, you'll just shoot the Beacon, so Aquila will only deal skill damage.
In that case, Aquila wants ATK and Skill Damage buffs:

Vidya - Celestial Swan
Vidya massive reduces the enemies DEF and Resistance, and buffs the teams damage a little too.
Vidya only debuffs the damage resistance of the damage type the enemy has most recently received.
As such, if using Celestial Swan, then make sure the other non-Vidya support isn't off-element to Bubu.
(i.e. They either deal Kinetic damage or do not deal damage at all).
Siris - Freefin
Freefin is a great skill damage support
Marian - Riptide
Riptide is still a good skill damage support, although off-element to Aquila
Eatchel - The Cub
Eatchel provides a nice ATK buff

Against single-targets, Aquila herself will deal quite a bit of damage with her SMG, but you'll generally want to foucs on the Skill Damage from her Beacon instead, so the above supports are still her best choices.

With that being said, Aquila does have literally unlimited ammo and a high-RoF SMG, so Tess - Phantasia can add a lot of damage to Aquila when she's shooting an enemy.
Aquila's signature SMGs have 30.66% Compatibility and a RoF of 950 shots/minute (15.83 shots/second), meaning Tess can add an awful lot of damage simply due to adding damage to each of Aquila's shots.
Aquila is off-element to Tess though (Tess adds Frost damage).
Fritia - Little Sunshine is a weaker version of Tess. Also off-element (Fritia adds Thermal damage).

Similarly, ballistic buffs aren't the worst for Aquila. Not ideal as they don't buff her skill damage, but they will work to a decent degree simply due to how many shots Aquila puts out.