I think you should make a modifier for a class you select in your player profile. You can change it but you can only select one at a time. You will not be penalized in any way for not selecting a class but you will get a "perk" if you will for the class you do select. You could have like a drop down with all the classes and a description of the perk or enhancement each class offers.

For example

Sniper - may get to hold breath longer and a scope available to him that is not available to any of the other classes.

Grenadier - May get to carry more grenades than the other classes and some type of enhancement to the grenade launcher.

Rifleman - may get better opportunities to shoot from the hip and a microdot in the aiming radical when firing from the hip.

(these are just examples)

Machine gunner - etc.
Medic - etc.
Engineer - etc.

I think this would really help to build a character that is a little more personal and tailored to reward your personal playing style and offer more diverse contributions to a team.