Marian - Queen of Pain (a.k.a. "QoP")

If you don't have Queen of Pain yet but want to try her out, she is available as a Trial Operative in Story Mission 1-7, as well as Chapter 5, Missions 1 to 3.

Queen of Pain is a pretty standard ADS sniper - just spam her ultimate and shoot stuff. Her dps is generally quite low and you do actually have to aim and land your shots, but she's easy to play and has good movement speed.
She's also a fantastic support operative for any operative that deals chaos damage.
If built correctly, she's a very strong chaos damage support, and one of the best 4* supports, although like all 4* operatives she performs poorly when compared to 5* support operatives, but for some specific 5* dps operatives QoP is still a very strong support.

The Basics

Role: Strong Chaos-damage support.
Deals Chaos Damage
Deals almost entirely ballistic damage
Mobility is... weird.
(Likes to be stationary, but her actual speed is high)

How to use Marian - Queen of Pain

As a main DPS:
Use her ult as often as you can
Spam her standard skill off-cooldown.
Otherwise just shoot stuff while ADS.
(Do not shoot hipfire shots - always ADS.)
As a support:
Spam her support skill off-cooldown.

How to use Marian - Queen of Pain

Weapon:
As a DPS: Mark of Mesmer / Chocolate Filling
As a support Deep Sea's Call / Disco Confusion
Weapon Parts: Max ATK

Logistics Squad:
As a DPS: Amano-Iwato
+10% ATK
+8.5% Chaos Damage
As a support: Twilight or Amarna
+19.3 Skill Haste
+10% ATK
+8.5% Chaos Damage
Best squadmates for Marian to support:
Any operative that deals Chaos damage

Passive Ability

Marian gains a passive ballistic damage buff whilst she is in ADS. (Called being in "Focus" state.)

Marian also gains ADS Ballistic Damage after she has been stationary for 1.5s.

Standard Skill

Marian deploys a phantom decoy for 8s that taunts nearby enemies.
Whilst the decoy is active, Marian gets +50% movement speed.

When Marian shoots, uses a skill, or the 8s timer ends, the decoy explodes and Marian loses her speed buff.

Her Neuronic buff increases the duration from 8 to 12s.
With her other Neuronic, while you are Disoriented (i.e. CCed) you can use her standard skill to clear that.

This skill doesn't really increase Marian's dps at all, although the extra movement speed is nice.

Ultimate Skill

Hold Marians ult to lock onto the targets weakspot, and deal high damage to them when released.
This can crit, and deals double damage to shields just like normal ballistic damage.
Given that weakspot hits always crit, this skill being able to crit means it will crit often, allowing for much higher dps than its damage numbers might initially suggest.

With her Neuronic, using her ult while her standard skill is active causes her decoy to deal additional damage.
This gives around 50% more base damage, but this additional damage is skill damage and can't crit so in practice it adds less than that.
Since this comes from the decoy itself, buffs to Marian don't affect it, only buffs to the decoy.
The high Crit Dmg value of Marian's sniper means that the ability to crit does add a lot of damage to her ult, so the extra damage from her Neuronic isn't much.
Maybe 15-20%. The more investment Marian has (good supports, more Manifestation levels, etc.) the lower the percentage of her ults damage this Neuronic deals.

The damage is fine for a 4*, and it can be used very quickly due to its 5s cooldown.
It's low-ish U-Energy cost of 50 means that it's more spammable than most ults, which also gives it pretty good dps for a 4* operative if it crits, but poor dps if it doesn't crit.

Support Skill

Marian just shoots the target, dealing high damage.
It gets +50% Final DMG if the target is unshielded.

With its first Neuronic, the damage increases by +100%, which is a large increase.

With its second Neuronic, hitting an unshielded target decreases its Chaos Resistance by 20% for 10 seconds, which is a very strong debuff.

This shot actually deals good damage, and with the debuff it's actually a really good support skill for supporting operatives that deal chaos damage.

Weapon

As a DPS:

Marian wants a Chaos damage sniper rifle.

Mark of Mesmer
+639 base ATK isn't overly high, but 181.26% Compatibility gives it very high damage per shot, with the weapons buff gives ADS Ballistic DMG and Crit DMG Amplifier.
Chocolate Filling
A Chaos damage sniper rifle that you can get for free from the reward track of Paradoxical Labyrinth.
The Compatibility stat isn't as high as Mark of Mesmer (152.59%), but it has much higher base ATK (798) and gives a nice ATK buff, as well as having a higher inherent ATK buff, and the extra chaos damage every 5s adds a good amount of damage.

Chocolate Filling has a higher ATK stat, and a higher inherent %ATK buff, but Mark of Mesmer has a higher compatibility stat that gives it higher inherent damage.
Due to her high per-shot damage and high crit damage value, Mark of Mesmers buffs can allow it to potentially deal more damage than Chocolate Filling.
Given that QoP is only a 4* operative, and that she isn't overly good as a main dps, you'll generally stop using her as a dps eventually anyway and only want to use her as a support, so there's little reason to invest into getting her a weapon so she can be used as a dps.
As such, if you do want to use her as a dps, then just which whichever chaos sniper you acquire first.

As a Support:

Deep Sea's Call [Deals Frost damage]
This gives the deployed operative an ATK buff for 15s based on Marian's ATK.
Since the ATK buff from Deep Sea's Call lasts 15s and QoPs Support Skill also has a 15s cooldown, you can maintain Deep Sea's Calls buff easily.
Disco Confusion
When dealing damage with a Support Skill, reduces the targets Chaos Resistance by 7.2-12% for 5s.
This damage reduction will stack with the resistance debuff from her Support Skills Neuronic, as well as from the Twilight logistics squad if you are using it, allowing Marian to inflict a huge chaos resistance debuff (20% +16" +12% = 48%), albeit briefly.

Which weapon you choose to use will depend on whether you want to buff your operatives or debuff the enemy, as well as which logistics squad you are using.
Due to the strong resistance debuff QoP already gives from her support skill, I generally recommend Deep Sea's Call rather than Disco Confusion, but both are good options.

If using Marian to support an operative that is very bursty - i.e. deals a lot of their damage over a very small time window, then Disco Confusion can be used to maximize damage during that short window. This works well for supporting operatives like Cherno - Enigma, as well as the Styx Envoy + Riptide combo to a lesser extent.

Logistics

As a DPS:

Amano-Iwato
After a crit, increases ADS ballistic damage by 10%, up to 5 stacks.
Since QoP is an ADS dps, if using her as a dps then Amano-Iwato is her best choice for logistics by a large margin.

As a Support:

Marians support skill deals damage and debuffs the enemies chaos resistance.

Twilight
When the operatives Support Skill deals damage, reduces the targets resistance to that damage type by 16% for 5s.
This is a strong albeit short buff, but QoPs resistance debuff means that QoP+Twilight gives a very significant chaos resistance debuff.
Amarna
After using their support skill, Amarna gives the entire squads ballistic damage by 30% for 15s.
This is useful to support operatives that primarily deal chaos ballistic damage.
This basically limits QoP to supporting Fritia - Turbo.
This makes Amarna a very niche choice, but if you are using QoP to support Turbo then Amarna is a good choice for QoP.
Given how niche this is, Twilight is generally the better choice, and still works well with Turbo.

Logistics stats:

Given that QoPs chaos damage resistance debuff only lasts 10 seconds, but has a 15s cooldown, QoP really wants Skill Haste to maximize the uptime on her debuff.
For her 3rd stat, the only useful stat for her is +8.5% Chaos Damage.
Beyond that, the other stats don't really fundamentally change how she is played.
S-Energy Recovery can be useful to maintain her S-Energy levels over longer fights, but isn't necessary, and with stronger dps operatives potentially not useful at all.
QoPs best logistics stats are +19.3 Skill Haste, +10.0% ATK, and +8.5% Chaos Damage

Manifestation

M1 gives QoP +100% Final Damage when Marian is stealthed by her standard skill.
This does actually give QoP a damage increase for using her standard skill, and as such if you have M1 you should spam her standard skill as often as you can.
M2 gives QoP 1 extra Focus stack every second she is in ADS, up to 9 stacks.
Each stack of Focus gives a +12% good ballistic damage buff, so an extra 9 stacks is a huge damage buff.
In practice you'll just ADS, magdump, and repeat, and due to Marian's low magazine capacity the average buff is much lower than 9 stacks, but it's still a large damage buff.
The stacks being lost upon shooting means they're mostly for preparation rather than to provide a consistent dps buff.
M3 Gives QoP 1 stack of Focus per 0.5 seconds.
Again, given that each stack of Focus gives a large damage buff, this can translate to a huge damage buff.
In practice you are better off shooting frequently rather than waiting to stack the buff, but you can pre-cast before a boss spawns so you have a lot of stacks for your first shot.
M4 gives her standard skill +1 level, and increases the damage bonus her Focus state gives to 14%
M5 gives Marian +20% chaos damage dealt when Marian is within 15 metres of the decoy spawned by her standard skill.
Since this is a damage taken effect, this is very strong.

Being a 4* operative, you'll max all her Manifestations eventually.

Good Teammates for Marian - Queen of Pain

If Marian is used as a DPS:
Marian's low per-shot damage means she doesn't really gain much damage from per-shot bonuses like those provided by Phantasia or Little Sunshine.
She does deal some skill damage, but the vast majority of her damage is ballistic, meaning skill damage buffs aren't overly useful for her.
Instead, she mostly wants generic ballistic damage buffs, as well as supports who can provide generic or chaos damage resistance debuffs.

Yao - Nightglow
Yao's ATK and ballistic damage buffs are very useful for QoP.
Marian's high crit damage value means that Yao's crit damage mods are very strong for Marian.
Vidya - Celestial Swan (and other resistance shredders)
Celestial Swan and other resistance shredders (Acacia - Kaguya, etc.) that reduce the enemies resistance help enemies take more damage.
If using Celestial Swan, make sure the other support isn't off element to Enigma.
Fenny - Starshine
Fennys ballistic damage buffs are useful for Marian, and not needing to reload allows her to stay in ADS for longer, increasing her buffs and damage.
Eatchel - The Cub
A Blitzing Fangs Eatchel provides healing as well as a decent ATK buff.
Not the strongest support, but still good.
Mauxir - Shadow Ka
More damage, and a target that doesn't move.
Shadow Ka is also on-element to Enigma, so you can use Enigma + Shadow Ka + Celestial Swan if you wish.
Fenny - Coronet
Cornet's RoF buff is a nice buff for Marian.

Since there really aren't any 4* supports that actually help Marian to any significant degree, and basically all 5* operatives will out-damage her, you're generally best off not using Marian as a DPS.

If Marian is used as a support:
Marian provides a strong chaos damage resistance debuff, allowing her to support any operative that deals chaos damage without exception.

If used with Deep Sea's Call and Amarna, she can work as a very good support for Fritia - Turbo, who likes the ATK and ballistic buffs, and the chaos damage resistance debuffing.

If used with Twilight squad, QoP can be used as a strong support for Cherno - Enigma, as Cherno's damage being concentrated into her standard skill detonation means that even short duration buffs can be a huge dps increase to Cherno.
To a similar but lesser degree, QoP can also be used to support Nerida - Styx Envoy with Marian - Riptide, who also deal a lot of chaos damage over a short period of time.

QoP can also be used as a support for Acacia - [Redacted], who deals entirely chaos damage, increasing Acacia's damage by a large margin.