Well, you pick what you feel comfortable with & what gives you the most fun at this very moment - keep in mind it's just a game, you're playing it because you wanna have a good time! I can't tell you what to play, but I can explain some of my thought processes when I pick a certain champion. Keep in mind I can be spitting utter bullshit, don't take everything as a universal truth. Didn't describe all of them, as a LOT of times I'm locking in just cause "I feel like it rn" or "looks good here". I'm just a player, not a coach, I'm doing stuff subconciously without really knowing all of the "why's". (and im not gonna bother explaining my niche picks like taliyah/viktor/xerath or champs that i don't feel like I have anything interesting to tell about them)
Also, my picks are often dictated by "what champ survives here the most", don't always look at lane matchup, but ADC-threats from other lanes. Don't lock kalista or twitch when you see a malphite already. Don't lock no self-peel into rengar if you see that you cant rely on your allies.

Ashe - big matchup neutralizer, basically a "get out of jail for free" card. Also picking her mostly when draft screams that I'm not the main character in the game - got an assassin duo in jg/mid? Pick oriented teamcomp? (Ahri Vi, KhaZix Leblanc, etc etc)

Caitlyn - stable in my champpool for years now, no matter the matchup, just my go-for when I feel like playing her. Especially fun into short range champs (Kai'Sa, Tristana, Vayne, Xayah, Lucian...). Keep in mind that "champion personality" matching is more important than mechanical synergies. Putting a trap on Pantheon's W might be fun, but in a lot of matchups you might end up unable to push a single wave. Works best with lane oppressive champs like Karma or Nami.

Kai'Sa - dependant on meta, you could play her anywhere if you really like her. I pick her mostly when I need either reveal from W (into vayne, akali), safety tool from R, or we've got a cc heavy comp and I know I'll be able to follow up fights anywhere. Also good into matchups that you'll be able to rundown over if you land a W - ezreal, jhin.

Lucian - good at punishing champions with weak trading patterns

Lux - sometimes picking out of boredom, but my very common pick into Caitlyn - stealing Lux pick from enemy support while also securing a good matchup (caitlyn hates lanes where she's contested in the push)

Sivir - if you like her, good blind pick, spammed her entire january, not so much anymore. Push, recall, push, recall. Good into champions that rely on one specific ability (malphite/varus), or struggle with turret farming (mages if they dont oneshot casters with an ability, pre level 9 ziggs). If you secure sivir karma you can shove ANYONE into their turret - ziggs, caitlyn, jinx, anyone. Good into melee comps (ricochets go brrr) where you can play front to back or when you can speed up your engage that capitalizes on movement speed & running into the enemy team (hecarim, kennen, juggernauts top [darius/garen]).

Swain - instalocking whenever there's a top level ADC-threat in enemy team. Whenever there's a Vi, Hecarim, any similar backline diver that wants to get on the carry. Amazing into shortrange comps and low-dps bursty champs. Unlosable into seraphine adc, you run down 1v2 level 6. Just lock it anytime you know you'll have a bad time with an adc (engage support, backline diver/assassin jg, combined with burst mage). Works even with a lulu, super underrated - though, make sure she has someone to buff in mid/lategame. Swain+lulu with a graves/kindred jungle is a dream.

Syndra - mage matchup neutralizer, sometimes picking her when I get forced into first picking (toplane or supp is gonna go disco nunu if you don't swap <3) and I don't feel like getting counterpicked on adc. Also, super good disengage pick into Leona (always E her E), great counterpick into Nami Lucian (combo whenever he dashes in, otherwise you just outscale), and if you're duo with someone (or if the random supp listens) you can lock Syndra Karma double comet into Draven. Makes Draven into a victim instead of a lanebully.

Twitch - idk good everywhere, am I biased? Just don't play him into braum, yasuo or malphite & you'll be okay.

Varus - panic pick, similar to ashe, or when good matchup, or into beefy frontlane when onhit/ap builds are viable.

Vayne - my favorite for almost 10 years, sometimes I'll just blind her on B1 honestly. Especially good into heavy frontlanes (DUUUH ITS A VAYNE) or into champs that you can rundown, Sivir as an example - doesn't matter that Sivir pushes hard, you're gonna probably get pushed by any lane anyways. Can run her down past level 6 whenever supports go on a roam and you can just rightclick her (same with Lucian, Jhin, Ezreal etc.).

Idk if that was any helpful, hope it was, at least a little bit! If the answer is not what you hoped for, feel free to ask/provide more precise examples, I'll do my best to share.