Currently in patch 10.10, there has only been 4 viable comps to me as there is a lot of donkey/hyper-rolls involved. It could be fun or stressful depending on the kind of player you are. Overall, I think it’s been fun despite the struggle to climb. The 4 comps that I will list below is Mech-Infiltrators, Brawler/Blasters, Void/Brawler, and Hyper-Roll Celestials (Pikachu/Shredder).
Demolitionist – Rumble/Kai’Sa(Demolitionist’s Charge)
Mech-Pilots - Annie/Rumble/Fizz
Valkyrie – Kayle/Kai’Sa
Infiltrator – Shaco/Kai’Sa/Fizz/Kha’Zix(Or Ekko)
Sorcerer – Annie/Lux
What you want to do here is to start off with a Chain Vest ideally. Getting a Bramble/Titan's Resolve is the best possible start. Best case is starting off early with a level 2 Poppy/Malphite and slap the Bramble on them. They’re tanky and will benefit the most out of the item before you put it on your Mech-Pilots(On Rumble). The hardest part about this comp is to obtain Fizz, which could make you take more damage than you need to. You should really try to hit level 6 post stage 3 carousel(3-5) and having Sorcerer is better than having Valkyrie. Before that, try to hold off and try to get a strong board even without synergy. Aside from Bramble, try to get a Titan’s Resolve and QSS or Dragon’s Claw. Kai’Sa will be considered as your secondary carry. You should try your best to get a Demo-Spat for her so that she can synergize with Rumble(AOE stuns!). Even if you can’t, it’s not the end of the world, it’s just nice to have….. but you really do want Morello’s on her and Seraph’s(if you can’t get enough tears, just any mana item would help). You can sub Kai’Zix out for Ekko later on in the game.
Blaster – Graves/Ezreal/Miss Fortune/Jinx
Brawler – Malphite/Cho’Gath/Vi/Blitzcrank
Mercenary – Miss Fortune
Starship – A.Sol(If you got space for him)
Chrono – Ezreal/Blitzcrank
Rebel – Jinx/Malphite/A.Sol(If you manage to get to level 9 or get a Rebel Spat(put it on Miss Fortune if you can))
Brawler/Blasters is simple, it's been the same and the most consistent throughout all the patches. You want to rush level 8 with this comp. You want to start off with a Red-Buff if you are going to play this since it’s really good for the blaster synergy. You want to stack your items early onto Lucian(great early/mid game carry). Your main carry will be Jinx and your secondary will be Miss Fortune. For late games, you want Graves over Lucian for the Blaster synergy because Smoke Screen is just so broken(seriously Riot?.....). Perfect items for Jinx would be Two Giant Slayer and one defensive item being Guardian Angel, QSS or Trap Claw. You might want to consider a Last Whisper with the amount of people playing Tanky Vanguards nowadays as well. After you sell Lucian, you probably will be putting the Red-Buff onto Ezreal or Miss Fortune, whichever is fine. Miss Fortune 1 is kind of whatever but her level 2 is really strong. Best case is getting a mana item(Seraph’s) for her and QSS. If you have extra items laying around, try to make a Guardian Angel and Ionic Spark for Cho’Gath.
Brawler – Cho’Gath/Blitzcrank/Malphite/Vi
Void – Cho’Gath/Kha’Zix/Vel’Koz
Chrono – Blitzcrank/Twisted-Fate
Mystic – Sona/Lulu(For level 9)
Sorcerer – Twisted-Fate/Vel’Koz
You want tears, a lot of tears, and more tears. Slam all your tears onto Sona as soon as possible. Seraph’s and Chalice of Favor are you choice of items. Sona will cast instantly every second and will be constantly pumping mana while healing(with cleanse(OP!)) your team. After gearing Sona, you want to put Morello’s onto your Vel’Koz(keep them together next to Sona always) along with QSS and Deathcap(for more damage). Pretty straight forward, the only hard part is getting all the tears. You want to rush level 8 for this, hopefully by 4-3.
Mana-Reaver – Kassadin/Irelia
Celestial – Kassadin/Ashe -> Lulu/Xayah/Rakan
Chrono – Caitlyn/Shen
Mystic – Lulu/Soraka
Protector – Jarvan IV/Rakan
Blademaster – Irelia/Xayah/Shen
Xayah will be your hard carry, make her as strong as possible early and roll for her, 3 star is a must. You would start rolling at 3-1 for Xayah/Jarvan/Caitlyn. You want Last Whisper before anything else, after that, it’s Infinity Edge and Guardian Angel/QSS/Trap Claw(You won’t need to worry about healing once you have your Celestial Synergies). Your extra items are to be dumped onto Rakan or Jarvan so they can “tank” for you. Morello’s and Shojin is great for Rakan and Zz’Rot/Bramble/Cyclone is pretty good for Jarvan, just any tanky items. AP towards Jarvan does increase the attack speed for the team, so it's not a bad ideal to get a DeathCap on him, but only if you have too many large rods. It’ll all vary what random/extra pieces you have left.
I currently have the most fun playing the Hyper-Roll Celestial comp, so I would highly recommend you trying out that build first! For every TFT patch, the meta shifts quite abit, so be sure to keep yourself update! But for the meanwhile, you'll have lots of fun with any of these comps listed above.