Hello I was thinking about getting a bolt action rifle but cannot decide what caliber to get. Shoot mostly recreational but would like to do some ground hog shooting. 17hmr possibly or just 223?
Do you have a .22 long rifle? If not, that is still a good place to start and more than a few groundhogs have been killed with it. Even though ammo is a little scarce right now I would still start with it, especially if you plan to do a significant amount of plinking. Otherwise, I'd personally get a .223. Plentiful ammo and plenty of oomph for longer range recreational use and varmints. I think Savage has some pretty cool bolt-guns in .223 that would be fun for some semi-precise shooting as well as hunting.
If you generalize across all game in North America, the best all around rifle is going to start at the 270 and range into the 30 caliber non-magnums. Something small enough to not be totally overkill on smaller game, but large enough for elk or bear in a pinch. The 30 is especially versatile due to the wide variety in bullets. I load my 300WM from a 200gr Accubond for elk out west all the way down to a 110gr VMax at 3800fps for coyotes in Indiana.
For Indiana, for what regular rifles are legal for here, I'd argue a .243 or some other 6mm variant. .223 is just a bit small for me, I enjoy longer range target shooting.
Pretty sure the most expensive caliber to shoot would actually be 22lr since it can't be found and the price is expected to go up. I'd say anything else that you go to the store and find sitting on the shelf would be a much better option.
7mm-08 or 7x57 are the first two that sprang to mind when I read the original post. Defining "all around" is going to have a considerable influence on the OP's choice, though.
If you ever want to hunt I would go .243 win. If you are just target and popping ground hogs maybe a .22 mag or other rimfire that catches your eye. Savage or Ruger would be my top two makers.
If you hand load I would steer you a different way into .223 or 22-250
In your broad question, a .50 BMG is the best all around caliber. It will shoot from 20 yards to 1500 yards and kill or punch holes in anything in its way.
22lr is great for close range plinking if you can find ammo. The 17hmr is a deadly little critter killer with great accuracy. 200-300 yards is no problem. A buddy and I were shooting glass beer bottle across a dried out pond at 200-225 yards with ease. Milk jugs at 300 are pretty easy. 223 is even better with alot more punch but I dont think you will find anything much better for the bullet cost and midrange accuracy if your ust plinking and its available everywhere. It depends on what your plans are more than anything and your price range on the gun and especially the ammo.
An AR15 in 300 blackout is a nice choice too. If they ever change the law to allow 30 cal for hunting deer, I'm sure it would be included. It works for a lot of other game too. Although the .223 works well for a lot of smaller game, the 300 blackout would work for them all, and deer should they approve it some day. Down side of 300 blackout is the price of ammo. I suppose you could buy it in .223, and buy a 300 blackout upper later. Bolt Carrier would swap out with no modifications. If you are wanting more range than a few hundred yards, you can't beat the 308 for a good rifle.
Embrace the latest fad and jump into a 17WSM w/ a Savage B.Mag and your choice of Boyd's stocks (cause the Savage one that came on mine was terrible, which seems to be a trend on these)