My top 3 favorite kits per class.
Adept
1. N7 Fury: http://kalence.drupa...13L54384!G9DB3G Always a fun kit to mess around with.
2. Drell: http://kalence.drupa...!13O54384!E.FEG Alternatively with Talon. Amazing at nuking spawns or sweeping groups of enemies.
3. Krogan: http://kalence.drupa...34053384!GF9B3P Either N7 Piranha or the Wraith, though am not a fan of the Wraith. Very durable and the combos hit like Optimus Prime if he were dual-wielding massive trucks as weapons.
Soldier
1. Turian Havoc: http://kalence.drupa...24W53364!95GA5K Either Incendiary or Disruptor ammo. Warp if the rest of the team are biotics. Basically is a vanguard who can recharge shields whenever needed instead of needing to charge to get them back. Extremely handy and dunks everything.
2. Krogan: http://kalence.drupa...24W53364!A50E5H Sturdy and can use the inferno grenade/Reegar cheese. Rarely use him because of it but when I'm feeling like cheesing things, I'll pick this guy. REALLY strong against armor even if not using Reegar cheese.
3. Vanilla Human: http://kalence.drupa...24W53364!F37AGG Just annihilates everything. Claymore works too. Only problematic enemy are phantoms on-host, and grenades usually handle them if you can keep them flipping.
Engineer
1. Volus: http://kalence.drupa...43C52314!GB9B3O Either recharge speed or geth scanner for gear. Really squishy but if used right and with right-hand advantage, you kill stuff ridiculously fast. Crowd control machine AND can cloak/restore shields. Very handy.
2. Male Quarian: http://kalence.drupa...24O52314!9EAB3G Crazy grenadier. So long as you have grenades to spare, you're a tech combo machine. When it comes to bosses, just scan, strip the shields with arc grenade and dunk with your pistol.
3. Geth: http://kalence.drupa...13053364!5F9A59 Is like the Geth Inf for me but without cloak. Wrecks things, can heal if needed or point out where an enemy is hiding if you're looking for them and is stupidly fast. Have it set up this way in case I switch weapons. Usually use GPS though.
Sentinel
1. Turian: http://kalence.drupa...24852314!6F9A3O This kit is ridiculous(also can you tell I love the Redeemer-I mean Arc Pistol?). Strip shields, warp armor, shoot in-between. Just all-around dunks everything and can be ready for every situation. The only downside? Can't dodge... 
2. Vanilla Krogan: http://kalence.drupa...24556314!G.9A8H This or replace Javelin with Black Widow or Arc Pistol. Reegar on shields, melee when appropriate. If armored units, use other weapon if possible. If not, MELEE(again, when appropriate). MMMRAH
3. Krogan Warlord: http://kalence.drupa...24556334!GA.D8H For those times when you just wanna bonk stuff with a gigantic hammer.
Infiltrator
1. Turian: http://kalence.drupa...24Z51364!G59A5G Arguably the safest kit to play imo. Doesn't kill everything as fast as, say, the geth inf but still can hold his own and solo whatever with relative ease.
2. Male Quarian: http://kalence.drupa...24W53364!59AA5O Raider or Claymore. Just like the MQE, annihilates spawns and the shotgun(s) dunk everything else. AND he can dodge, or hop, but still. Helps.
3. Drell: http://kalence.drupa...13053364!G.EAGK With either of those guns used, not at the same time though. Prefer shotgun. Very good CC with that and recon mine. Perfect system where you can cycle stagger shots of the GPS in-between Recon Mine nukes. That and he's a drell so insta-awesome in my book.
Vanguard
1. N7 Slayer: http://kalence.drupa...34N52364!E0.EGG (alternatively use Cyclonic Mods for more survivability) Amazing synergy with Phase Disruptor and Talon shots. can also jump through walls. Love this kit so much.
2. Drell: http://kalence.drupa...13O52364!E.8AGG Basically the N7 Slayer but way cooler and the grenades can nuke spawns quickly. Alternatively can use a shotgun but I like lower cooldowns for the Drell.
3. Vanilla Human: http://kalence.drupa...34957384!G.8DGK (Used VI because I have 100+ and only use the reegar to drain shields/barriers. Bosses have big heads usually) This guy is amazing when paired with a team that can prime/detonate biotic and tech stuff. Usage of Nova Cancelling will keep you alive while you have low cooldowns and just detonate everyone's primes.
My 3 least favorite kits
1. Cabal Vanguard. Just don't like her. I do better with the vanguards listed above.
2. N7 Shadow. If I wanna melee I'll be one of the Krogan Sentinels or the Krogan Vanguard. Just don't like the kit.
3. Turian Saboteur. Don't like any of his 3 powers. I perform better with either of the other 2 jet turians...or anyone else for that matter.
Edit: TL;DR: Every drell you can play as, I listed as one of my favs. Love them all. Drellguard mostly.