Is there a reason you want to stay .22 cal? What's wrong with a .308 or 30-06? Both of those calibers are 1000 yard capable without a lot of work. You'll spend more on optics than the weapon. Fwiw, I have .223 and 30-06 in my house. .223 because it relatively cheap to shoot (nothing's cheap to shoot the past 18 months or so), and 30-06 because my whole family has those and they are a very capable round (but literally 100 years old--WWI era)
I loaded some 22-250 for a friend and it used up 40 grains (it was a while ago-not sure how accurate that is). Anyway, my 30-06 likes 46 grains. There's a LOT of pressure getting that 22-250 moving the speeds it does. The 22-250 is very cool and incredibly fast but there are other factors to consider when shooting one. Your ammo is quite scarce and about the same price as a 30-06 or .308. It has very interesting ballistics but not the knockdown power (if you're a hunter) of the .30 cal rounds (that are easier to find ammo for).
There are some very interesting calibers to shoot out there now. 6.5, 300 blackout, .204 etc that are worth checking out for various reasons. For off the shelf, I'd stick with the ancient 30-06 round or the military available .308 or .223 just for availability of ammo.