I had a couple .22-250s that I used for targets, using it to win lots of turkey shoots. It shot lots of woodchucks, crows, and other varmints also. The thing I didn't like about it was the wind deflection at 300+ yds., plus the lack of feedback on misses.
One day, before we had rangefinders, my buddy and I shot half a box of ammo each at a woodchuck on a side-hill mound in long grass. We couldn't see our misses and ended up pacing off the distance, which we thought was about 225 yards. It turned out being over 300 yds.
When we started woodchuck hunting, it was to improve our shooting in practice for deer hunting. I had a .30-06 Savage 110 with a custom stock and a Weaver K 2.5x. The great thing about using it was that we could see our misses because it usually threw up a lot of dirt on impact. It enabled me to make a 500 yard woodchuck kill on the second shot.
That said, if I'd started with a .243 Win, or 6mm Rem, I'd probably been much happier. Wind in Maine during spring chuck season is very high and often unpredictable, due to woods and hills. Using 85 grain bullets, the 6mm is a great varmint caliber and it tends to throw up some dirt on misses. It may not be great for prairie dogs, due to recoil, etc., but hard to beat here on chucks and crows, (if there were any chucks left in fields).