Sounds like you’ll hunt similarly to how I hunt.

For a $500 or less hunting scope, I think there are several good options. This isn’t an exhaustive list as I’m not an authority. Just some scopes I’m familiar with.

Used Trijicon Accupoint 2.5-10x56. New may not be much more than $600.

New GPO Passion 4x 3-12x56 can be bought for $500 delivered tyd. It has a German #4 reticle. I like the one I just bought.

If you can get a used Meopta Meostar for $500, they’re awesome in lowlight.

I also really like my Zeiss Conquest DL 3-12x50. I think you may find one used in that price range.

All of the above have 30mm tubes. I personally like how they look. Personal preference.

I really like the large objective lens. It makes a big difference for lowlight hunting. I know scopes don’t
“gather” light. But, I sure see more with my 56mm than my 42 in the same glass.

Happy hunting!