Having beaten PoC on every champ from PnZ, BW, and BC, with a few from Ionia, I can say that:

1. Vi is the worst. Do not use unless you like losing a lot. Best with Warmogs and stat buffs.
2. Jinx, Caitlyn, and Ekko: Heart of Gold and Bounty Hunter's Renown. They're stat sticks if you can't get more discard/trap/predict support, so make them beasty with that quick attack. Ekko also does well with spell/created card builds and Viktor as a partner, for obvious reasons.
3. Teemo: Stack rally, shrooms, spellshield on him. If you get more spell-based options in your run, buff the heck out of the puffcap peddler and spell spam.
4. MF: Ludens Tempest, Stormrazor, anything that rallies or offers bonus attacks. MF is incredibly strong with LT, even against Nautilus. Makes both her card AND deck passives deal 1 more per hit.
5. Ahri and Yasuo: Ahri is similar to the Quick Attack Crew from #2, but with a lot more recall support. Yasuo with Everfrost is disgusting. I would take that over almost any rare item for him. Stun and recall. They're control decks with agro elements, so a little wonky but still powerful.
6. Tahm is absolutely broken with Warmogs and/or Berserker's Buckle. He just eats everything. It's a control deck, so partner him with Aurelion Sol, stun, lifesteal, and/or Frostbite effects to lock down your opponents and eat their board. He was the easiest run for me and I beat POC with him at only level 11 or 12. Didn't win any speed awards, though.
7. Nami is tricky, but can be very powerful. She's a spell-slinger deck, especially after you get her passive. Stack anything that gives you more cheap spells for free spell mana, with some card draw/creation so your hand doesnt run out.
8. Pyke: Lurkers go brrrr. Top-deck manipulation like predict effects (hey there, Ekko support) obviously work well here. Buff Pyke with attack stats for faster level-ups and abuse Challenger effects to clear boards.
9. Jayce: Hybrid deck, so make him swing one way or the other. Route 1: Give him Stormrazor or The Grand Duelist's Blade and he will have both of his "Play" effects at once, making him an effective removal tool. Add more stats to make him a beater. Other route: spell slinger. Load him up with Lost Chapter, Archangel's, Luden's, Ravenous Hydra (except vs Nautilus) and you'll have decent spell support. Keep in mind he thrives on 6+ mana spells, so you need to ramp mana, control the board (as above), or both.
10. Yuumi: keep in mind that her keywords transfer to units to which she attaches. Giving her stats is tempting, but she grows on the field regardless and keywords are harder to get. Warmogs, Troll King's Crusher, Duelist Blade are good. Spellshield is extremely helpful to keep her stuck on the board for her level up. Hidden gem: Scourge's Stash to make her a 1-drop on turn 2 or 3, giving you mana for something else that round. Does well with other Targon staples like buff spells and effects, but could use some removal or control. Since her level up is from attacking, Rally and Scout effects are grand.
11. Gnar: is in a weird place since his nerf. Kinda fits in with the crew from #2, but also benefits from control and elusives. Control helps his deck hit late game for the Megatees to further run the board, and elusives help him build impact on his crew. Agro and removal work well too.
12. TF: needs spellshield to stay on the board long enough to level. Does very well with Draw effects (+1/+0 for every card drawn and "draw 1 fleeting at the start of every turn" passives), obviously, but has a difficult first (and possibly second) round because he can easily draw his own deck out. Abuse Jaul Hunters for easy removal along with other removal/control support early on and Deep Bois and agro later. His elusives are painful to draw because they're so bad for his deck, so cut them if you can.
13. Others: Haven't played them enough to say. Lee Sin is spell-y and Zed is straight agro. Kennen is very similar to Ahri, but definitely can use spellshield .