I have used probably every conceivable caliber for hunting 'hogs: .22LR, .22 Mag, .22 Hornet, .223 Rem, 22-250, .243, 6.5x55, .270, 30-06, .308, .357 Magnum, .45 Colt, and I even shot one with a .458 Win Mag once!
My personal favourite is a toss-up between the .223 and the 22-250. I own Savage Heavy Barrel rifles in both calibers and they are both outstandingly accurate. Bullet of choice for both is 50 grain Hornady V-Max.
The 22-250 has an edge over the .223 in terms of speed and flat trajectory. However, the .223 uses less powder and actually gives up little to the 22-250 when fired out of a long-barreled bolt action.
I've had spotty luck with the .22LR on hogs; they get pretty big, particularly around this time of year and can be hard to put down with the rimfire.
For a new shooter, I would probably go with the .223 Remington in a good quality bolt action with a heavy barrel; ammuntion is cheaper, it is more miserly of powder when you reload, and brass is in abundance everywhere.
You can check out my posting about my last groundhog shoot (some real monsters pictured there!):
http://www.canadiangunnutz.com/forum/showthread.php?t=99619&highlight=summer