I was in the same boat, and I purchased a right handed rifle as talked about in this post:
ORIGINAL: confusedsoul
My dad and I are both left handed shooters. My dad owns a LH Browning A-bolt Medallion in 7mm Rem Mag with BOSS system and I must say it is a BEAUTIFUL rifle. A great shooter as well. With that said, I myself purchased a Browning X-Bolt Hunter in .270. Growing up I have gotten use to shooting right handed bolt rifles and it doesn't bother me to own one. Now if this would be a varmint rifle I probably would've held out for LH or semi auto rifle just for the handiness of cycling the bolt for a second shot. With big game, its usually one shot downed animal, so a followup isn't necessary. My X-Bolt is lighter, better trigger, better recoil pad, removeable magazine and is just as good a shooter. It doesn't look near as nice but I could've went with the Medallion version and been closer. I say go Browning, but either make a good rifle.
I'd also like to reiterate that for my varmint rifle, I will go LH or semi auto due to cycling the rifle more often.