I've been hunting with a hammer sxs of one kind or another for 52 yrs, mostly lower end Euro guns. Mine are all hunting guns and I hunt salt water estuaries out here on the coast, no sense wrecking a nice collectable quality gun. The pair I'm using now are Husqvarna 51's built in the 1940's with 2.5" chambers in 12ga, nothing fancy but rock solid and dependable plus there are a lot of parts available if needed. I hunted grouse and ducks with a Berretta Hammer O/U MZL for a number of years before steel became mandatory, thinking about taking it out again with some ITX. I even did predator control work in WI in the 1960's with a hammer drilling, a couple of years ago I picked up a back action drilling just like the one I used to use, hope to get it on some birds and predators next season.
With your budget you should be able to find a very nice Hammer SxS that you could feel very comfortable showing up at any bird camp or event.
If you see one that interests you, get pictures and ask about it here, these guys will help you find just the right one and keep you from getting burned.
