Are you looking for one gun or one gun with a combination of barrels? I'm a lefty myself and I shoot one gun. I shoot a Browning BPS. It's ambidextrous, has a tang safety and shucks the shells out the bottom. It's an older model with a regular Invector choke system. With a good turkey choke, it'll put 20-30 pellets into the head and neck of a turkey target at 40 yd. With an improved cylinder tube, it'll put Brennecke slugs into 4" at 100 yd. any time.
Whether or not you'd consider a left handed gun, I'd recommend any gun with a tang safety. I shot a Remington auto for years and unless you get the safety switched to lefty, it's a pain in the @$$ to get at the safety easily. If you are looking for one gun/barrel, I'd stay away from over or back-bored guns. They won't shoot slugs. I'd also recommend a 24 or 26" barrel. It is a nice compromise between a smoother swinging, longer barrel and a more compact gun for turkeys or deer. My gun has a 28" barrel and although I like the longer sighting plane, there are times I wish it was shorter. With the improvements in rifled slug barrels, A multi-barrel combo might be the way to go. A rifled barrel will be way more accurate that a smooth bore, and with a cantilever mount, you'll be able to put a scope on it.