I've been playing on regular, and beyond a tough early start, it's been pretty easy. Ever since I got the ability to mind control people with my Psi Operative.... damn.
I went with 2 rangers (easily the most helpful for the entire duration of my playthrough). 2 heavy weapons guys, 1 sniper, and 1 mech person.
Why no Specialist? They're actually pretty good. Far better than Supports were in the first XCOM.
I suppose on lower difficulties your squad configuration doesn't matter as much. And what you have going for deals a ton of damage. But if you want to try a higher difficulty, you'll probably want to use Specialists more often.
I assumed Mech Person = Specialist?
I don't think the party configuration is that bad. Did you change out depending on the mission? Sometimes Snipers are just useless, and it's better to have a second Specialist over having a Sniper, for example.
Oh by mech person I thought he meant the Spark that was added in one of the DLCs. Also, Sharpshooters are probably the second best class in the game if you make them Gunslingers. Just behind Phantom Rangers in my opinion. ---
Ah, yes, the Negotiator: General Kenobi <sneaky beeping>