I'm a lefty myself and I shoot a right handed AR with no problems. You really do not need a left handed AR as long as you have a shell deflector, which pretty much all ARs have. The only time you'd want a left handed AR is if your rifle does not have a shell deflector or if you are running it suppressed.
If you want a 308 AR then the DPMS LR308 seems to be popular. If you want an AR that is a bit smaller/lighter then you could go with the 300 Blackout. It uses a standard 223/556 lower receiver so you could have a 5.56 upper for plinking and a 300 Blackout upper for hunting. Those 308 ARs are pretty big.