If you are open to used doubles, I would consider both the V. Bernardelli sxs and the AYA 4/53.
I own a Gamecock 20 gauge with DT and extractors that has done yeoman service for over 40 years. That's a fairly basic gun, but there are a fair number of the higher grade guns out there within your stated budget.
I've owned an AYA 4/53 28 gauge for about 7 or 8 years. It's been a delight to shoot and completely trouble free. The new ones exceed your price point, but there are a number of used ones available within your budget listed on line.
Have fun with your search.
