Cross Dominate Eye and hand
My screen name is Left eye Dominate for a reason
I was well in to my 20s before I discovered why I could not hit a barn wall from inside the barn with a shotgun but could hit a running rabbit with a pistol. Mother was a left hand, Dad was Right handed, I got the mix left eye dominated and right handed. Yes there are people that are left hand and right eye dominate.
You will shoot better in the long run shooting off the shoulder of the dominate eye. Yes I can shoot right or left handed, but without a doubt shooting left handed produces better scores and hits. Forget eye-patches, taped glass and trying to retrain you eye dominance.
What to shoot?
1. Right handed on the left shoulder
Lefties have been shooting right hand rifles forever... Reaching over with your left hand to throw the bolt is not much of a trick. Reloading is a little slower till you get the hand of it. If you can choose a rifle without a rollover cheek piece all the better. FYI there are left handed stock for right handed rifles, the check well is on the right side of the stock.
2. Left hand Bolt action.
I prefer left handed bolt action rifles. A rifle that fit you and the way you shoot can not be under estimated. For the money this is my list
a. Savage Left hand rifle are the best deal going.
B. Remington 700 left hand are great and not to hard to find
C. Winchester finally started making model 70 left handed.
D. Weatherby Mark V left hand
E. all other left hand bolts
3. Lever action,
A. Winchester, ,
B Marlin, Pre-cross bolt safety
C. Browning BLR,
D. Savage 99 .
4.Single Shot
A.Ruger #1,
B. Browning
C. TC Encore/ Contender
D. NEFHandi rifles
5. All others
Left hand ARs ect
Just do a search on Gunbroker for all the other left hand rifles.