Oh, you have opened a HUGE can of squiggly critters with this one. IMHO it depends on the range of hunting you plan on doing and what part of the US of A you live in. Gound hogs and prarie dogs are possible with a .300 win mag but, it will wear you out. .220 swift will kill a bear or moose but, I sure would not try it.
For me (central Texas) .25-06 will do for anything from yotes and jackalopes up to the wiley 120 lb white tails we have. It will do for prong horn and mule deer too. It would be a bit dicey on elk but, with a good bullet (Nosler partition) and a well placed shot certainly not out of the question.
If I lived in Maine or Idaho, I would not even own a .25-06.
Best over all? My guess would be .270 Win or .280 Rem.
Also a good idea to check state law where you will be hunting. Some states don't allow some things which other states do. Some states only allow shotguns with slugs for deer, and of course shot is better for birds.
A rifle,hands down would be my choice..Unless state law prohibits it..Especially a bolt Action rifle,theres no need for semi automatic,because if you miss the first shot,unless you're good at the "Run and Gun"..then your target is as good as gone anyway.
Rifles are so much more accurate to me than a shotgun,granted,theres no replacement for a good ol' American 12 gauge pump. But they aren't my prefered method of harvesting meat.
Personally,I use the Mosin Nagant M44 for my hunting needs,good range,reliability,awesome acuracy. Weight is somewhat an issue,but if you have a rest that eliminates that. Plus the stopping power,for what you need it to do. Is overall decent.
Unless of course,you live in Indiana,and such guns are illegal to hunt with,then you pull out your Winchester 12 Gauge and your good to go. But if you have a choice,then a rifle would be the first thing I'd pack.
The simple answer is nothing is good for alround hunting if you are talking about squirrel to moose, unless your willing to keep your shots on moose to around 75 ydrs., then it would be a shotgun with a smooth bore baeerl and another rifled barrel.
since we don't know where you live, I assume a rifle is an option I would suggjest a good bolt action chambered in 7mm-08 Remington After a butload of research and lots of math I think It is one of the best cal's out there with out all the magnum BS that you probably don't need It has better ballistics than a 308 and is a dream to shoot, very low recoil, if you lived out west I would lean more to a 270 or 30-06, 30-06 being my choice just cause of the longer distances you would be shooting, that being said a shotgun is by far the most universal of the two, it is only good for close range unless you use slugs or sabots, really depends what your needs are?
Ballistically, the 7mm-08 and the 280 are the best of the bunch with there superior ballistic coefficent (ability to cut through air), very efficent sectional density, and tight twist rates, I would lean more toward the 7mm-08 because the recoil is almost a carbon copy of a 120gr 25-06