RB, for the price range you are wanting to be in, you'd be looking more toward a break open type gun. Plenty accurate but cant shoot the stiffer powder charges like you can with a bolt gun. Range is more limited.
I would like to know why there would be any difference between a bolt or a break action as far pressure.
My thoughts would be the only rear thrust would be on the bolt or action face on a break action would be primer, nothing else can move to create rear thrust. Not like a centerfire cartridge that the cartridge has rear thrust and can move, because it is containing rear pressure against the bolt lugs or action face and hinge pin on a break action.