That budget depends on what you get - and whether new or used. I had a .22 Benchrest rifle built by a great gunsmith, used top-line components, and it cost a bit more than that without scope, mounts, tuner or ammo. I used a L/H Stiller Copperhead action, Krieger barrel, Jewell trigger, Shehan African Obeche laminate Tracker stock, Kelbly rings and bases, March 8-80x scope, etc. That was well before COVID, so I'd guess the prices higher now. With the March scope I put on it ($3,400 alone at the time I bought it), test ammo, tuner, plus another case of ammo that it liked - and it was somewhere north of $7,500 for everything I don't know how much used .22 rifles of a similar build (which I think is typical of serious rifles) like mine would run - but I'm guessing there would be a fair discount involved. It always seemed to me that center-fire benchrest rifles built right by a good gunsmith with good components typically resells for the cost of what it would take to build the rifle, less the cost of a new barrel. I think that most people assume the barrel was no good, yet don't typically want to pay more than what it would cost for a new rifle after barrel replacement. They still get a used rifle, yet forgo waiting time for acquisition of components and the gunsmith wait time. Mistreated rifles sell for far less. Rimfire barrels last SO much longer, I doubt the "cost minus barrel" method of appraisal works the same with a .22 rimfire. It would be a good idea to research the typical resale prices through some rimfire dealers who specialize in such rifles. Some of the others noted a few above. Perhaps they don't depreciate such as center-fire. I'll be looking at those as well - trying to figure out what is a reasonable price for my own rifle.
I built my rifle specifically for local club matches and before the rifle was completed, the nearby range sold, and they promptly quit have such matches there. It has been a safe queen ever since and I'll likely be selling mine on this site before long - to include a case of Black Box ammo for someone who can pick up the ammo locally I'll also be selling associated rimfire gear like rim thickness gauge, concentricity gauges, etc., etc.