My safe is occupied by LH Remington and Ruger bolt actions, Marlin lever actions and a couple of right hand pump shotguns. A little off topic from your original question, but Browning and Ithaca make a couple of really nice bottom eject pump shotguns that fit lefties quite nicely. Mossberg, although ejecting on the right side have made their controls left friendly, and Remington makes a couple of dedicated left hand shotguns.
Jeff270 has pretty well rounded out the manufacturers. Price wise, new lefties will sometimes cost you a hundred bucks more than the right hand version, and they are harder to find. I have never felt I paid a premium for any I bought used. You do have to be patient but deals do occasionally surface. If you are looking for a specific chambering that can be a pain. Most of the lefties you find on the racks in gun stores will be in .243 Win, .270 Win, 30-06, or .300 Win mag., any of which would do fine as a deer rifle. Tikka is one of the most left friendly manufacturers and offer many different chamberings in left hand, but my guess is you would have to special order anything other than the most popular chamberings.
Older Remington BDLs and Marlin levers come equipped with useable iron sights. Most newer bolt actions don't, but all are easily scoped.
I grew up shooting my fathers right handed bolt action rifles. I got along quite nicely and it is an option, but I do find I prefer a true left hander as a hunting rifle.