If budget is an aspect we can find both of those in so many models, BUT I'm not an expert on these matters; your budget, do you want to use it for deer hunts as well, your local hunt regs, etc.. Some of the Remingtons from the 80s in semi-auto for the .243, or even the 6mms; not sure where the ammo costs are on 6mm today... I CAN say that with the 22-250s you want to look at the gun's barrel twist rates, and which are the better weight of the pills. IE; I just found a weird Ruger No.1V (varmint) from 1976 with a 26" barrel, and that twist rate prefers the lighter (40-50gr) for accuracy. If you want pelt preservation of some sort, I'd go with 22-250's smaller holes. Not sure which year it was, but one of my uncles had a 22-250 in a Rem. 700 bolt gun IIRC, and it was a tack driver.
Now, if you don't mind buying blind on GunBroker, there's a little glitch in the systems right now; following an auction via your phone hasn't worked for me lately. Which means the other buyers *probably* can't either, and so many people live/die by phone apps., so you can *accidentally* snipe some decent deals; look at sellers feedback #s, history of recent sales and what they've been selling. I'll look up some examples in GB....