Sharing the wealth after playing for a while now:
Berserker/Priest is a handy close support combo. Immunity to mind control, close combat with area effect offensive/defensive skills. I find it great for capturing enemies and buffing other front line troops. They are particularly adept at holding choke points and indoor infrastructure protection with panic and mind control, especially when outfitted with the screamer helmet. Lower their will on approach, clog the entrance with MC. Have another outfitted with the will +2 regen AOE helm behind them under cover and you have a living, sustainable wall of enemies to block their buddies. I have beat missions without ever having my team engage with weapons with this tactic while only using enemies to kill enemies. Then capturing the MC’d pawns at the end.
Sniper/Infiltrator is great as well. I look at them as the glass cannon of the game. Huge DPS potential with long range when hiding them in a flanking position away from the main engagement areas. Their damage buffs add up very quick and incapacitate enemies as well.
Heavy/Sniper is a great tool for getting a birds eye view of the majority of the map’s enemies on the first turn. I also ensure they are equipped with both regular and para-sniper rifles. These guys are really good for taking off the rocket launcher arms, shield arms, and regen/pain chameleon torsos due to their high ground perches. Lairs with close perches can also sometimes give you an immediate view of hatcheries you can hit from across the map without messing with the routing of troops to objective.
Assault/Infiltrator class is my go-to for research theft. I can (most times) take all three points before the enemy turn. If I cannot then they hide in a corner to get the last on the 2nd turn.
Infiltrator/Priest is great way to stack buffs on a defending position as they need minimal cover (sometimes none depending on stealth level) to regen troop will points. This allows supported units to really spam their abilities every turn. These guys are great to be around a heavy using Boom Blast as it turns them into a virtual MLRS every turn with grenades, grenade launcher and missiles (especially from high ground).