Find a smith that works on the old ones, they are harder to find than the guns are. Those folks will have some info on what you should look for, probably knows a couple clients that have some to check out.
Your price range is good for American 12 ga field models, most have 2 3/4” chambers after about 1920.
The stocks have more drop and cast than the modern stuff, and the wood is 100 years old. There are lots with small cracks in the wrist, and restocking them decreases the value.
I prefer to buy the restocked ones, modern geometry and new wood is more useful to me as a shooter. Better pricing too!
Good luck buying just one!
