If you don't wish to play as a Quarian infiltrator I would recommend a class with overload. Not only does it pop shields, on unshielded Geth it caused extra damage and makes them spazz out where you can get easy shots without fear of retaliating fire.
Shield stripper weapons such as Assault Rifles and SMG's are advisable as Geth rely on strong shields to protect them. Their health compared to other enemies is quite low.
Headshots on a Geth should be aimed at the optics as well as the "curved" part of the head. Nailing this will kill just about any Geth in one blow, even the Cloaked Hunters.
Rocket Troopers should always be a priority for any sniper. If left to their own devices they will wipe the players.
Geth Hunters, though tricky, aren't too much of a threat. Shooting them when they're cloaked will briefly give you a target lock. Anyone with overload can use the window to pop their shields, Geth Hunters without shields cannot cloak. Outside of shotgun range, they're just target practice.
Geth Pyros are absolutely fun to play with and make for easy grabs. You can simply lure a Pyro to any thin bit of cover by popping it a few times to make it walk up to your cover. They can't burn you so long as you're hiding and will just walk right up to you for an easy grab. Beware multiple Pyros though. They'll get smart enough to walk around your cover and fry you from two sides. So long as you stay out of flamethrower range or behind cover they can't quite walk around, they're nothing more than target practice.
Primes are EXTREMELY dangerous and should not be left to walk about unchecked. They do however suffer from head shots and with their ridiculous size and slow walk, are the easiest to hit. Bolt action sniper rifles to the head will make a Prime stagger 90% of the time. However such shots in quick succession WILL NOT stagger a Prime.