On my first ME play-through, I went with the entire suit of biotic classes: Vanguard, Adept and Sentinel in game order. On my next play-through, I'll end up doing the three I missed.

Vanguard changes rather drastically between ME1 and ME2/ME3. In ME1, it played for me as an adept with less skills (but good skills) but can wield a shotgun, prompting you to be more at the front lines. In ME2 and ME3, the introduction of Biotic Charge and Nova necessitates risky, close quarters game-play. It really does play differently. I'm not a fan of risky game-play so I didn't do Vanguard again in the sequels.

The Adept plays fairly similarly. You get all the biotic skills, but you're rather frail in combat. But I enjoyed the Sentinel the most. You get Tech Armor in ME2 and ME3 which really boosts your defenses, and you get the key offensive skills from both worlds: overload and warp.

I'd say the Sentinel is the best of the three I played, but I enjoyed the Adept as well. I can't really tell you about the Soldier, Engineer and Infiltrator classes, but I'm told the sniper stuff in ME1 aren't that great. I've never really been much of a stealth player either.