The problem for you is recoil . Cheap scopes tend to pack it in with heavy recoil .
I think you are going to need to spend more / maybe $2000 US . A Vortex Razor might be ok for about that price .
This video may help. https://www.youtube.com/watch?v=TRpBxLbxhAo
Turret caps are fairly useless on a long range gun and most scopes in that category don't have them because you will be cranking the vertical up and down quite a bit acquiring targets at changing ranges .
I have a Leupold VX-6 on my 338 Lapua Works flawlessly Great scope all around. For the money I feel it preforms better then other scopes I own/owned that are twice the price.
A lot depends on what features you want in a scope . I you are dead set on turret caps then that leads you to certain model scopes . If you want Mil graduations or FFP cross hair then that leads you to certain models . You have to write a list of the features you want and see which ones have them. Leupold is a good standby .