Have to claim two... Stoeger X20S and Crosman Nitro Venom, both in .22, both with upgraded "tuna" triggers and better scopes, these rifles have taken out a LOT of backyard pests.
Benjamin Nitro piston something or another in .22 gets the nod for the majority of yard work. Found it for $99 on clearance, I guess, and was a bit concerned, but it has proven itself time and time again.
My Avenger wasn't but a few $ over $295 when I bought it, and it is a gem. It comes in the .25 flavor.
The closest I have to your price limit is an HW30. I love that rifle. I’m sure that I have put more pellets through my HW30 this last year than all my other rifles combined. It’s perfect for a small backyard like mine.
Purchased new - Gauntlet .177 but really the purchase used AA410 (16mm shroud design) is all that and more. Still holding air and zero after 4 years and a cross country move.
i dont really think of a go to rifle in terms of money ...my needs are constantly evolving i would say, and i havent been 'into' getting more guns for very long, but still the marauders are my go to guns out of 12 guns now ... the P for most pesting and the rifle in .25 when i need to hit something big or hard .. the hatsan blitz is working its way in there i would say for 'special cases' lol .. we wont go into detail .. but 295 meh, i say save another check or two and get exactly what you want ...
My .177 bsa buccaneer is a gem and shoots the fx 10.3's at 920 for one hole groups at 25 and 1/2 inch at 50. Picked it up on eBay around christmas for 280 and have just been adoring it! Has a huma moderator on it and a truglo 4-14x44 scope. It's my absolute favorite gun to grab and plink with after work, and it's no slouch on the pests either. Best kill to date is a starling out of one of our trees at 73 yards.
My gamo urban. It falls just above that at 300 but it’s pretty close. Quality built, hand pump friendly and dead nuts accurate out to 50 yards. The best part is it loves all o go the crosman 14.3 grain variants. Pushes them around 875-880.