SWFA scopes have a very solid name if you planing to do a lot of turret turning for reaching out punching paper. Also their Black Friday sale is still in effect.
Vortex seems to also be a popular choice, although it seems to me that they are either sworn by or sworn at.
Leupold offers some models that may be within your budget.
Bushnell elites, in particular the elite tactical are an often over looked choice for your purposes.
The used market opens things up even further, the middle to high end German and European optics may be a possibility although I suspect Nightforce may still be out of your budget.
Your budget does leave you with lots of options, myself I'd look for a scope with a minimum of 4x for the low magnification if I am hunting. The 10ba is a very heavy rifle and you may only carry it a few times before looking for something lighter unless set blinds and/or longer range shots are your thing. So if you find a scope you like that has a base magnification of 6x I wouldn't sweat it, because I suspect you'd quickly get a dedicated hunting rifle it is something you enjoy.
Reticle is the real sticking point when it comes to target vs hunting scopes, I really like a simple target dot or mill dot scope with a very fine crass hair for targets. The downside is while precision placement is easier, it disappears against an animal in low light.
