I have found the Marlins to be quite accurate--the time-honored Marlin model 60 can be incredibly accurate, and fairly nice looking as well, with the little bit longer barrel, and a nice 3-9x scope included, for under $250!
Depending on what you want, and how you want to modify it, etc., you might look into an old Winchester 67, with a 27" barrel (assuming a fairly decent bore). Put a nice looking scope mount on it, and you might have something. Just for a lark (pun intended), I shot a mid-sized bird out at 50 yards with open sights several months ago, even with my old (58) eyes! I was almost surprised at the hit! Sometime I'll have to put the guns (I've got 2 Win. 67's) on a solid rest and see what they can really do!