Re: grocery shopping...
I really, really like my 1885 Browning High Wall in .45-70, but if I was looking for an all around white tail round, I'd stick with .243 Win or 6mm Remington.
I spent years hunting deer with shotgun slugs. Point of fact, at eleven, I harvested my first deer with an old single shot .410 and slug.
As far as damaging the meat, I harvested numerous deer with 12 ga. slugs with very little meat damage. There's a hole, but, for a placed heart-lung shot, you're only going through ribs and that's not a big deal.
For boar, wild feral pigs, etc., many kill the h-ll out of 'em with .223 Rem/5.6mm NATO. Many states don't feel them powerful enough to humanely harvest deer, but they drop pigs like nobody's business.
If you're hunting in heavily wooded areas, the good ol' fashioned .30-30 seems to be (from what I've read) a winner. I've only used 'em on 'yotes.