>>3764796>I have inherited an SLR and three lenses that use this mount
Can you post a picture of the SLR and the lenses?
Nikon lens compatibility is real tricksy. "F-mount" refers to everything from the original Nikon F from the 50s all the way up to the most modern digital SLRs, and there have been three or four fundamental changes between then and now that affect the compatibility.
Most notably, if the film SLR is old enough--I.e., from before the 1970s and using similarly old lenses that haven't been modified--then the lenses won't mount properly (and might break) higher-end modern DSLRs. If they're not autofocus, they won't meter on low-end modern DSLRs. If they're autofocus, they won't autofocus on low-end modern DSLRs. Etc.
So to know whether or not there's a DSLR in your price range that fits the bill, we'll need to know what your film SLR is. Post a picture of the camera and the rear mounts of the lenses you have, ideally.