All my play is via the 360 version, but here’s my take on character classes and party makeup:
Obviously if you’re a shooter-type player you’ll find a home in soldier. I’m assuming you’re asking about the other, more complicated classes.
Personally, I play as an infiltrator and love it. Though I’m limited to medium armor and can’t wield assault rifles and such, I’ve managed to find/buy such a bad-ass sniper rifle, pistol, and armor set that it’s not really a big deal. And being able to train the tech skills myself means that I no longer need to carry a tech-trained individual in my party to deal with locks and terminals – a further combat plus.
That said, Sean hates the sniper rifle – he’s a more charge in and stick a shotgun in the enemy’s face kinda guy – so he plays as a vanguard. That means he has more weapon options (including shotgun and assault rifle) plus some basic biotic powers. He can expound more upon the virtues of the vanguard, but I’ve seen him play and it’s clearly very effective for him.
One important piece of advice: don’t underestimate the power of biotics. I did, and it really held me back for a while. At the low levels, biotics seem slightly less effective than pure shooters, but at higher levels they’re mean as hell in combat. And a party combination of biotics and shooting is unbeatable.
If you’re new to the game, I’d definitely avoid the engineer class. Tech attacks are only marginally effective making this a very difficult class to play. Consider it for hardcore players only.
Though I’d probably advise waiting until your second character to start as an adept, if you’re patient there’s no reason not to go for it at the beginning. It’s a very different way of playing, but Sean and I have watched friends clear levels without firing a shot – purely by careful application of biotics.
Re: party makeup, I’d advise you to always think about the overall balance of the party. You’ll need someone with tech skills as a basic requirement or you’ll miss out on all the loot – and even some of the side missions. Beyond that, I believe your most powerful team consists of a good balance of biotics and shooters.
For example, as an infiltrator, my favorite combo is Wrex and Liara. (Yes, I know. I’ve made cracks about how I left Liara in the ship the whole time on my first and second playthrough. My bad. She’s incredible in a fight.) The enemy just doesn’t have a chance: they pop up, they immediately end up floating around the room (thanks for the lift, Liara!) while getting warped (thanks Liara and Wrex) and shot all to hell (thanks Wrex). If I manage to draw my own weapons fast enough, I can lower their shields with tech attacks and/or clean up the mess.
As a partial biotic, Sean likes to carry a tech/shooter and a full shooter or full biotic with him. As a shooter, I’d probably carry a tech/shooter and biotic.
The good news is that there are dozens of “right” ways to get there, and exploring to find the right one for your style is an important part of the game – just like handling situations via the dialog wheel. Sean and I are both pretty decent players, but we play via entirely different strategies.
Another piece of advice, though: train either charm or intimidate at every opportunity until one is completely maxed out – and I mean all the way to the right of the screen, not just maxed out to whatever boxes currently appear. I won’t spoil you by telling you why, but you’ll totally thank me for it later. Audra, for example, lost a week or more of gameply because she didn’t do this. (Technically she could have continued, but once you see what happens, you’ll understand why she went back.)