(Click on the character/operative name to go to the article on them.)
These are listed in order of my perception of their power - the stronger the operative then the closer to the top they are.
Chenxing - Jade Arc
The best sustained DPS in the game [by-far], with a very short rotation that allows her to be good over long or shorter fights
She also deals enough damage that you can stack arrows in enemies and one-shot many bosses, bypassing invuln effects for even faster clear times.
Katya - Dawnwing
Very strong and consistent sustained DPS.
Dawnwing's Ult is a big burst of damage, but you'll still need to charge it with Dawnwing's Crystals, so even with Tess she doesn't have much initial burst.
Dawnwing also has excellent mobility as you'll use her standard skill a lot in combat, which can move her a significant distance.
This extremely high mobility does help with her survivability, and she's probably one of the most survivable DPSers for a beginner to use because of this.
The main problem with Dawnwing is that she requires a lot of investment to get to the point of being excellent.
Without high investment, she's still good, but there may be better options.
Lyfe - IS
Lyfe puts out considerable single-target damage.
Her Ult is great against groups, but a DPS loss against single targets.
Lyfe's spams dodge constantly, so she has good mobility and survivability, which can make her very easy to play for newer players.
Lyfe's standard skill does increase her DPS quite a lot, but it's not a "burst" - Lyfe IS is just very consistent DPS.
Bubu - The Geomancer
Very strong and consistent DPS.
Bubu's Ultimate is her standing still doing burst-shots. She can move between these bursts, but her overall mobility is still very poor during her ultimate.
This quick movement between bursts also moves her aim, and keeping all shots on target whilst moving between Ultimate bursts does require some practice.
These two things can make her difficult to use for new players, although standing still is completely fine of course, more-so if you like being punched in the face.
Bubu doesn't really have any burst at all.
Katya - Rhapsody
Rhapsody delivers a mix of ballistic and skill damage (but mostly ballistic).
She does lack mobility, and whilst her minigun is very consistent, her Ult + standard skill are somewhat short-duration and bursty.
Nerida - Styx Envoy
Nerida's damage is mostly wrapped up in her Ultimate, making her damage extremely inconsistent and sporadic.
Since her Ultimate requires doing as much Chaos Skill damage as possible in a very short time period, Nerida requires Marian - Riptide as a support to work effectively.
Needing Riptide makes Nerida something of a one-trick pony - as teambuilding for her is very limited as Riptide is basically mandatory.
If you aren't/can't use Riptide alongside Styx, then I'd recommend against using Styx Envoy for any ranked or endgame content at all.
Enya - Tempest
Extremely high burst damage.
Her sustained DPS is respectable, but not nearly as good as many stronger operatives, such as Jade Arc or Dawnwing.
Many bosses only actually need one burst from Tempest though, in which case Tempest is basically the ideal operative.
If your Tempest isn't strong enough to kill the boss in one burst (and maybe a few standard skill casts) her performance drops significantly due to her mediocre normal dps.
Having Tess - The Magician to fuel an initial ultimate really helps Tempst, especially at medium investment.
Fritia - Turbo
Turbo spends most of her time in combat sprinting around, which gives her extreme mobility and thus survivability.
With max investment she'd be in the [bottom of the] above category, but without it she's pretty bad.
Notably, Turbo can only sustain her damage rotation if she has her 5* weapon. Without it you'll have to stop your rotation to recharge quite a lot.
Stopping your rotation because you ran out of stamina also kills her mobility and thus survivability, and Turbo is very squishy to begin with...
These make her feel catastrophically terrible to use in endgame content if you don't have her 5* weapon, so I can't in good conscious move her up a tier.
Turbo's incredible speed does also make her the fastest way of getting around Star Master maps, so if you want to 100% those then Turbo is your best bet.
Cherno - Enigma
Enigma deals very respectable damage. Not as good as the more modern DPS operatives above, but still perfectly fine.
Enigma works by deploying stationary black holes, which really don't work against bosses that are very mobile.
Against stationary bosses Enigma is fine, but against mobile bosses she's bad.
Siris - Ksana
Ksana's damage rotation is pretty slow, but her damage is still respectable.
She's also quite bulky, has pretty good mobility, and is quite easy to play..
Her damage just can't compete with the newer DPS operatives though.
Vidya - Celestial Swan
Vidya's Ult gives a permanent -Defence debuff to the targeted enemy, and her support skill gives a huge -res debuff to that enemy with extremely high uptime.
(Her support skill has unlimited uptime if she has her 5* weapon)
This allows vidya to debuff enemies by a significant amount, and Vidya is currently the best support in the game for essentially all builds by quite a margin.
The mechanics if her Support Skill mean that Vidya loses a lot of effectiveness when dealing multiple damage types to the enemy.
As such, if using Celestial Swan your main dps and your other support operative should deal the same type of damage (Kinetic, Thermal, Frost, Electrical, or Chaos)
(Note Celestial Swan herself doesn't deal damage, so she doesn't affect what you can use at all.)
Yao - Nightglow
Nightglow gives a significant ATK and ballistic damage buff to allies.
She's not as useful for skill-based characters, but her ATK buff means she's still ok
For ballistic characters Nightglow is incredible.
Fenny - Starshine
Starshine gives a decent ballistic damage buff, but using her support skill also gives you a special magazine.
This means that spamming Starshine's support skill means you don't ever have to reload.
Her ballistic damage buff is respectable, but most of her strength lies in your main operative never having to reload.
This also makes Starshine less useful for operatives that don't need to reload (e.g. Bubu), or who reload relatively infrequently (e.g. IS).
Similarly, for operatives with very small magazines, needing to constantly spam Starshine's support skill can be quite annoying.
Marian - Riptide
Riptide is a sub-DPS.
You use somebody else as a DPS, and their skill usage charges up Marian's skill. Once Marain is full, pop Marain's support skill, magdump, then swap your DPS back in.
Riptide's M2 gives the entire team +20% Skill Dmg for 8s whenever her Tidesong Shells increase or decrease. If you're using her as above, that's basically permanently.
Combined with her logistics set, she provides your team with a strong skill dmg buff.
This makes Marian quite useful for Skill-based DPSers, although she's useless as a dmg support for ballistic DPSers (although might still be useful just as extra DPS).
Marain tends to work really well as a support for certain characters, and is basically useless for basically everybody else.
Acacia - Kaguya
Kaguya gives a nice -resistance debuff that is good for all operatives regardless of damage type.
She isn't as strong as Celestial Swan, but still good.
Acacia does also give a +Frost buff, meaning she works best with operatives that deal Frost damage.
This is a minor buff, and most of her buffs are generic and affect all operatives, but Acacia is still best used with frost operatives.
Acacia tends to be mutually exclusive with Celestial Swan - you can use both of them at the same time (with a Frost DPS) but that's basically never optimal.
Enya - Exuvia
Exuvia increases allies skill damage.
Shooting whilst Exuvia is active also gives stacks that buff the next skill used with extra Electrical Damage.
Needing to shoot does limit Exuvia, as characters like Styx Envoy just don't ever shoot, but Exuvia is still good for skill-based characters if they can shoot sometimes.
Quite a few of the most recent operatives don't ever shoot their guns (Nerida, Tempest, Clarina...), meaning Exuvia doesn't perform very well with them.
(Exuvia can still work, but your main DPS interrupting their DPS rotation to shop and shoot their gun just to get Exuvia's bonus is not optimal.)
Whilst Exuvia is primarily a skill-dps buffer, she's only really useful for operatives that shoot their guns a decent amount.
Tess - The Magician
The Magician is a U-Energy battery.
... That's it.
She's ideal if you only need one Ultimate (e.g. Tempest) or need to use an Ultimate quickly or frequently for some reason.
For characters that live-or-die by their Ultimate (e.g. Hush) Tess is fantastic due to her U-Energy buffing.
For characters whose ult isn't that much of a DPS increase, Tess isn't that strong.
For sustained DPS Tess is usually not a great choice.
Note that some characters literally cannot use U-Energy at all (e.g. Bubu or Clarina), so Tess doesn't provide them much benefit at all.
Tess - Phantasia
Phantasia's Support Skill gives shots extra Frost [aptitude] damage.
Phantasia's Ultimate skill gives extra Frost damage to aptitudes, and extra ballistic damage.
This makes her very strong for ballistic characters that deal Frost damage, strong for ballistic characters, and utterly useless for purely skill-based characters.
Vidya - Agave
Agave is a Parts Breaker.
If you actually need a strong Parts Breaker, then Agave is always your first pick.
She's ideal for casual content play, but for endgame content outside of Parts Breaking she just doesn't have the damage to be a strong main dps.
Note that healers are not needed at endgame, but are still nice for casual content, minigames, and other event content.
Eatchel - The Cub
Eatchel gives a generic damage buff on use of her support skill.
She's popular as a support though as NOT using her support skill causes her to passively heal the deployed operative each second.
Eatchel is the best healer in the game by a huge margin.
Endgame players don't need a healer, and Eatchel is only a decent support, but for new players Eatchel is likely one of the best supports just so you don't die.
At endgame, Eatchel can be used as an ATK buffer, but this is entirely due to her 5* weapon (Blitzing Fangs) and M1, and without those she's just a healer.
Yao - Quiet Quitter
QQ is just there to deploy her drone that gives PBAoE healing.
She doesn't ever buff you or debuff enemies - she just heals.
She's good at healing, though not as strong or as consistent as Eatchel.
The slowness of her drone makes her difficult to use with characters that move around a lot (Turbo, Clarina, Styx, Dawnwing, and IS are probably the worst offenders).
Since QQ is a purple-tier operative, she's generally the best healer that new players will have access to.
QQ will work fine as a healer, but eventually you won't need a healer at all, and if you do then Eatchel is just a flatly better healer.
You only ever need two teams in Snowbreak, so Eatchel and QQ are the two healers you should use, should you actually need healers.
There really aren't any other healers that are in the same league as Eatchel or QQ anyway...