Re: Which Caliber
If you're looking for a prairie dog rifle, a .22/250 or .220Swift is a nice long-range compliment to a .223. You won't get off as many rounds before heating the barrel up though so plan on slowing your pace compared to the .223.
For a short-range compliment, I'd check out a good little .22Hornet. Sounds like you're looking for a longer range rig, but they're cheap to feed and you can shoot one all day and hardly warm the barrel up.
I'm running .204 for my long-range varmint rifle right now. On paper and in the field, a 32gr .204 is near-identical to a 55gr .22/250 in velocity/trjectory/windage and a 40gr .204 is not much slower.
I've taken 'yotes out to 200yds with the .204 and it drops em just as dead as the .22/250. 200yds is my personal limit, I never liked shooting beyond that with the .22/250, Swift, or .22/6mm.
If you want something different, one of the .223-sized 6mms (6x47mm, etc) might be something to check out too.
A little heavier bullet, but it'll carry good energy out to 200yds+ for varmints & coyote/fox hunting. Would even be usable on whitetails at 100yds or so.