I can understand your position.
.223 will do the job...and will be quite abit cheaper on ammo.
22-250/220 swift will do the job as well. They're a step up from the .223 but you pay for it in ammo price and availability
.243 will work also. Not quite as flat as the 22-250 but wind drift will be same until you get WAAAAY out there.
270, 7mm-08,308,30-06...these are all waaay overkill but would not be 'bad' choices and would give you an "all-around" rifle for everything. Recoil will become an issue with these things though if you plan to sit down and shoot alot of hogs. Since it sounds like you've got alot more groundhogs I'd go the .223 or 22-250 route. I'd look at a stevens bolt before I did the H&R....but this is ONLY because I've heard they don't do as well with the high-pressure rounds. 22-250 and 243 would definately be considered high pressure...not sure about .223.

Best of luck. Be sure to alot some decent money for a scope. It's a shame to put a $40 scope on even a cheap gun unless its absolutely necassary. You cant shoot what you cant see and the low-light situations are when you 'get what you pay for'.