I would look for a scope that has at least 3.5" of eye relief. More is sometimes better but there are always trade-off issues, so I would stick with something in the 3.5" - 4" range.

A 40mm objective (not a 50mm) would be my choice for the front end. You can mount a 40mm lower to get a better cheek weld, and 40mm scopes weigh less and usually cost less.

If your $500 budget includes the cost of good rings and bases you might want to look at something like a 4x12 VX-2 for a scope. There is a good selection of quality scopes in the $300+ range from established manufacturers. Any way you cut it you will want good quality rings and bases. Rings and bases are important.