Another good option I've used left handed is a right hand bolt with a left hand thumb hole stock. I have a 338-06 that was (supposedly) built by PO Ackley on a RH model 70 action an in some ways it makes even more sense than a LH bolt because you never have to let go. Somewhere I have some paperwork on its provenance, but regardless of who built it it is a really neat idea that works very well.
Left eye dominant, always shot right handed guns, usually semi-auto so I didn't have to worry about cycling. Started shooting bolt action a couple years ago, found that I can tilt the gun toward the left and reach over and cycle fairly quickly. I have practiced it, but it hasn't been necessary yet while hunting.
I shot right-hand rifles for a long time, as there was not much for selection for left-handed shooters. I still own one right-hand rifle and I have no problem with either. When buying right-handed rifles, the only critical item is getting the stock to fit.
The one advantage to a right-hand rifle, is that if you try to sell it, it will sell faster.
