Sounds like to me that you would do great as a sentinel and a soldier. Vangaurd is more up close and personal combat tactics with BC and nova, and as infiltrator I usually stayed behind cover. Don't know about the engineer but I think it's similar to the infiltrator in staying back and letting the drone and turret distract as you dish out the damage. And adept focuses more on casting powers than dealing damage with weapons.
The sentinel preaty much has the best universal powers for default (overload, warp, throw, cryo blast, etc.). I would reccomend trying this class out at least in ME2 since tech armor is ungodly more powerful than the tech armor in ME3. A good thing about the sentinel in ME3 is that, like a soldier, it can carry two heavy weapons without dealing a lot of damage towards power cooldowns. With my sentinel, I went with the Lancer X and Reager X with 70% cooldown penalty (from tech armor and fortification) and still had +115% cooldown (185% with the weapon weights). So dishing out the bullets while still maintaining a decent cooldown rate is, personally, my favorite and best way to go.
The Soldier is also impressive. It mostly focuses on weapon damage and ammo powers. If you role with a soldier class, I would definetly put points in all the ammo powers especially incendiary and cryo ammo. And the squad ammo power evo on those two are preaty key in both ME2 and ME3 to dish out a lot of damage from all around. I usualy keep disrupter ammo to myself and only use it against synthetics like the geth or an atlas. Concussive shot is also viable. Especially if you choose the amplification evo which will give your CS the power of what you are using as your current ammo. RedCaeser97 made a good thread about the
Amplification Power on CS. There is one particulary trick he explains that lets you basically spam fire explosions with the incendiary ammo. And Adreneline rush just slows down the speed of your surroundings so you can unload more bullets into your enemies as well as giving you a damage reduction. Honestly, I only used the adreneline rush power for surivability and run to cover so I wouldn't die. You can't use powers with it on, unless you choose the power evo. And as the sentinel, you can carry some heavy weapons with you without putting too much strain on your cooldowns.
Well those are my two reccomendations. Start with one and do the other and see how you like them both.