222 for me. I have had 22-250's. Keyword is had. Currently have 2 -223's and one 222.
You will love how nice the triple deuce is to shoot, pretty easy to watch your impacts, and doesn't burn barrels out like the 22-250.
Super cheap to reload, lighter grain bullets put coyotes down with authority out to reasonable ranges. Still factory rounds available, just not as many options.
Lapua brass is available for it, which is a selling point for some guys. Definitely wouldn't buy a savage axis in 22-250. Some savages are good, but the quality control is pretty dismal on those, and the stocks and magazines are super cheap.
Lots of guys saying 22ARC, definitely a good option, would be my first option as well. But I'm a 6.5 Grendel and 6mm ARC fan.