With that budget, the first thing I would do is call around locally and see what you can find used. Specifically, ask if they have any small, composite, TL rated safes.
We sell a number of used safes like this in the $1,000 to $1,500 range. They have good fire ratings, and true burglary ratings.
New, the types of safes that you would be looking at would be B rate fire/burglary safes. A B rate safe would be a few steps down from a TL rated unit, but there are some decent options for those as well. Don't be swayed by price alone, as in many cases you get exactly what you pay for, but there are some decent imported units that run less than the US made offerings.
I tend to prefer the mass produced commercial type units over the more "custom" types offered from some of the smaller companies.