Permanent Banners

Snowbreak has two gacha banners that are always available:

[Operative] Duty's Command
[Weapon] Heart of Midgard

Each banner has a fixed and limited number of rewards that it can give, and these are always the same.
Rewards are not added to these banners as time goes on and new operatives/weapons are added to the game. Again - these banners always stay the same.

You will slowly get pulls for both of these banners from various sources.
The game does also very rarely give out a selector crate for one of the two that lets you pick one of its 5* rewards.

So which reward should you pick?

Firstly - Snowbreak has very little in the way of endgame content that requires a strong team with lots of investment and knowledge of the games mechanics, and any 5* operative will be capable of clearing all of the games non-endgame content with ease if build correctly and with a bit of investment into them.
This means that any literally operative is fine for literally 99% of the games content.
Even for that endgame content, the additional rewards you get from making a super strong team instead of just using whatever you find lying around behind the sofa are small.
It is perfectly fine to use whatever operative you find the most fun or appealing.

Further note that Snowbreak has had quite a bit of powercreep since the 5*s in the permanent banners were introduced, and none of the 5*s from the standard banner are great by modern meta standards.
As such, there's a good chance you'll stop using the 5* operatives in the standard banner when you get one of the newer 5* operatives who is much more effective.
If you only want to use the most effective operatives, you will stop using the 5* operatives in the standard banner quite quickly as you get newer and better 5* operatives.
As such, which operative you will want to go with can depend on whether you want a fun operative or a very strong operative.

This article will give a brief explanation of how each of the operatives play, who each of the weapons work well with, and what I think are fun and what I think are good picks, although which you find most fun is entirely subjective, and again - picking the most fun operative is entirely fine for almost all content.

[Operative Banner] Duty's Command

This banner can give you one of the following 5 operatives:

Lyfe - Wild Hunt [Frost-damage Main-DPS] Try Lyfe in Story Missions 7-12 and 10-12
Lyfe has a high Rate-of-Fire SMG, and her skill causes her to fire Frost Projectiles at the target, dealing ok damage and some AoE.
With her M1 Manifestation buff (which requires either 1 dupe pull of her or 30 days of collecting from her Personal File) she can fire the projectiles continuously.
Wild Hunt plays a bit differently after she gets her M1 buff, as she no longer needs to constantly use her standard skill - use it once and then just fire with her SMG.
Wild Hunt is a very easy-to-play operative with a simple rotation, good damage, and good mobility, although not the best range.
I'd consider Wild Hunt to be the most versatile and universal Main DPS out of the 5, and she is my general recommendation if you want to use your pull as your main DPS.
Marian - Swift [Kinetic-damage Main-DPS] Try Marian in Story Mission 5-12
Marian has a sniper rifle, but her skills mean that she generally hipfires it rather than needing to ADS.
Her sniper gives her good range, her ability to not need to ADS mean that aiming and playing with her tends to be relatively easy too.
Marian is a Main-DPS, but Swift has essentiallyno AoE capabilities and her DPS isn't great either.
Marian is the middle ground between the RoF and mobility of Wild Hunt and the range and damage of Winter Solstice.
Even with high investment Swift is clunky to play, and since she benefits a lot from having high investment, for new players I recommend you don't use or pull for Swift.
(I don't recommend Swift at all, but especially for new players.)
Fritia - Hush [Thermal-damage Main-DPS] Try Fritia in Story Missions 8-12 and 11-12
Hush has an Assault Rifle that deals ok damage with a good Rate-of-Fire over good range.
Since all of Hush's buffs are for her ultimate skill though, her assault rifle doesn't really end up doing much damage.
Once Hush is max-level and has some investment, her Assault Rifle isn't very strong at all.
Hush spends most of her time in combat ineffectually shooting stuff to build Ultimate-Energy for her ultimate skill.
Hush's ultimate skill fires a giant controllable laser beam at the target, which deals increased damage the longer it goes on for.
With a lot of investment Hush's ultimate can do very high damage and last a long time (15s+), but if Hush doesn't have much investment her dps can be atrocious.
Hush is an all or nothing operative - either be willing to go all-out on her and give her loads of investment, or don't use her at all.
Hush requires too much investment to be good as your first DPS, so I don't recommend Hush as your first 5* Main-DPS.
You're better off with your first dps being effective immediately, rather than needing tons of investment before they become respectable.
Yao - Winter Solstice [Thermal-damage Main-DPS] Try Yao in Story Mission 9-12
Winter Solstice is an ADS sniper.
You use her Standard Skill to chamber a special round, ADS, aim for the enemies weakspot, then shoot.
Winter Solstice used to be the games queen of DPS (a very long time ago) and she deals by-far the highest dps of any of the 5 operatives here.
Spending most of her time in combat in ADS means her mobility (and thus survivability) isn't great.
She also has no AoE at all - she's single-target only. For endgame content that's fine, but for most of the games content Yao's lack of AoE means she's slow to clear groups.
Yao doesn't have the AoE for me to recommend her as your main DPS, but if you just want max damage for endgame content or bosses, she's the best of the 5.
Fenny - Coronet [Electric-damage Main-DPS and Ballistic-Support] Try Fenny in Story Missions 7-12
Coronet uses a shotgun, which deals lots of weak hits.
Fenny has a low RoF, requires you to be at short range, and has to reload often.
Personally, I think Fenny is the most fun of the 5, but Wild Hunt is a better all-rounder.
Dealing lots of hits makes Fenny good at breaking destructible parts on enemies.
Fennys Support Skill provides a RoF buff, meaning Fenny is the only one of the 5 that can provide any form of useful support functionality.
As such, even if you don't use Fenny as a main DPS you can still use her as a parts breaker and RoF support for your ballistic operatives.
Fenny is thus a good pick, as even when you get another 5* that's either more effective or that you like more, Fenny can still potentially be useful as a support.

TL:DR
If you want an operative that is strong and will work well as your main operative that you use, then pick Lyfe - Wild Hunt
If you want an operative that works the best for endgame content, then pick Yao - Winter Solstice
If you want a very strong operative, then you'll use the first modern 5* you get, not one of the five above, so pick Fenny - Coronet here, as she works best as a support.

[Weapon Banner] Heart of Midgard

This banner can give 5* weapons.
Each of these weapons is the optimal endgame weapon for a specific operative - some are for 5* operatives, and some are for 4* operatives.
Some weapons are decent on other operatives as well, but eventually those other operatives will get their own ideal weapons.
If you really like one of the associated operatives, you should get their associated weapon.
If you don't want to use any of the associated operatives, there isn't much point pulling for any of these weapons, and you may as well save the pulls for the future when you might want one of them.

This banner can give you one of the following 10 weapons:

Stardust Memory Frost-damage SMG [Associated Operative: Lyfe - Wild Hunt]
Gives skill damage bonuses.
It can be used by the 4* operative Mauxir - Meow, but Stardust Memory is the ideal weapon for Lyfe - Wild Hunt only - no other operative really finds it ideal.
Horn of the Orca Kinetic-damage Sniper [Associated Operative: Marian - Swift]
Replenishing 1 bullet when a hipfire shot hits a target makes this extremely good for Marian.
Since Marian is the only operative in the game who wants to Hipfire with a Kinetic-damage Semi-Auto Sniper Rifle, Horn of the Orca is only really usable by Marian.
Lava Bones Thermal-damage Assault Rifle [Associated Operative: Fritia - Hush]
Gives bonuses to ultimate damage and skill damage to burned enemies.
Due to Hush's all-or-nothing playstyle, Lava Bones is really useful for her.
The 4* operative Fritia - Little Sunshine can make use of Lava Bones, but Little Sunshine is best used as a support using Strawberry Shortcake instead of Lava Bones.
Space Cowboy Thermal-damage Sniper [Associated Operative: Yao - Winter Solstice]
Space Cowboy gives a huge Ballistic damage boost after reloading, which Yao's standard skill counts as.
Space Cowboy is thus very strong for Yao, as she's the only operative who reloads before/after every shot, and it's not very good for every other operative.
Sunny Payback Electric-damage Shotgun [Associated Operative: Fenny - Coronet]
Sunny Payback shoots an extra shotgun pellet, allowing for more damage and better Parts Breaking.
The extra pellet is useful, but no other operatives want Sunny Payback as their ideal weapon.
The only other operative who can use Sunny Payback is Mia - Starshine, but due to the weird way she works Mia is better off with her 4* weapon than Sunny Payback.
100 Battle Veteran Chaos-damage SMG [Associated Operative: Cherno - Those Two]
Bullets deal extra damage as the magazine capacity depletes.
100BV's extra damage is useful for all operative, and thus 100BV can be given to any operative who uses an SMG.
100BV is often better than the designated 4* weapon for most SMG operatives, and hence is a good spare SMG to use for new operatives until they get their designated 5*.
Tiny Grains Kinetic-damage Shotgun [Associated Operative: Fenny - Lionheart and Nita - Hands ]
Tiny Grains' proc can be difficult to make work with many shotgun operative, as you need to get hit consistently.
Lionheart and Hands tend to stay in melee range, making the proc easy to proc for them, but for other operatives Tiny Grains' proc is difficult to use.
Having high damage means that Tiny Grains works well for all shotgun users, especially ones dealing kinetic damage, but is only ideal for Lionheart and Hands.
Olympus Frost-damage Sniper [Associated Operative: Yao - WInter Solstice*]
Olympus is not an ideal weapon for any operative - it works for Yao, but isn't her ideal weapon (which is Deep Sea's Call).
As such, I don't recommend you aim to get Olympus at all.
You may have gotten Olympus as an event reward, but Olympus is only useful if you don't have anything better.
Trial's Eve Electric-damage Assault Rifle [Associated Operative: Chenxing - The Observer]
Trial's Eve gives an ATK buff for 5s when you are healed.
With some investment, Chenxing can maintain this buff permanently.
The ATK buff from Trial's Eve is slightly less than the 4* weapon Strawberry Shortcake, and thus Strawberry Shortcake is better, but only slightly (20% vs 22% ATK)
Since Trial's Eve does also give +ATK is allows Chenxing to heal more, but that's usually a secondary concern.
Trial's Eve is fine, but many people will prefer to use Strawberry Shortcake, which is also easier to get as it's a 4* weapon and not a 5*.
As such, I don't recommend you actively try and get Trial's Eve - it's fine, but it's not really any better than the 4* Strawberry Shortcake.
Star Ocean Kinetic-damage Pistol [Associated Operative: Haru - The Ace]
Star Ocean gives a 3s Kinetic DoT when a skill hits a target.
Star Ocean is very good for Haru - The Ace, and works well for Haru - Absconditus as well.
Both The Ace and Absconditus are weak operatives though, so unless you're a huge Haru fan then you're likely better focusing on one of the stronger 5* operatives instead.