Hey so yeah, I got a sweet laptop and was using my buddy's steam account to play this: beat it once on normal (only reloaded one time because i lost the terror mission where you first meet chryssalids) and only lost two missions, and am about halfway through classic mode. I've reset classic mode a good number of times.
I like to play online with a single sniper psi-assassin, and two drones to scout with. FUN.
I'd recommend you be a little more cautious. Keep your men together with as many on overwatch as you can, rather than having them charge into a room containing mutons. It would be less Brikwarsy, however.