For something completely different, how about a Martini in 22 Hornet or the like. They make wonderfully light, handy open (or aperture) sighted rifles, the trigger can be gotten to superb (many of them are already very good) and you'd have the pleasure of commissioning (building) something that will be special and unique. @akaroa1 has photos of an excellent example. They are not "expensive" projects unless you go mad so one within or close to your budget would be possible