Easy, it depends on what ya wanna do with it. Shottie is a great cave defender, but overall length can be detrimental to close quarter combat, which is why some go with sawed off bbls. (Of course how many short bbld shotguns do you see employed by entry teams?) Ever wonder why the border patrol 'needs' them? I could be wrong, but if your shotgun leaves the factory with a pistol grip, you can pay the tax for an AOW - any other weapon- to shorten the bbl. The cost - $15? If the shotgun leaves the factory with the full stock then I think you need to go the normal title II route - $200 for the tax stamp to legally shorten the barrel. Then of course you need to realize that a short bbld shotgun is going to be LOUD - as in KABOOM - but so will the .223.
Rifle, I guess you are looking at most versatile here, not long range like a .308. Here I'd say the best bet would be a Bushmaster. Has the cool factor but also a lot easier to control than the shotgun. The shottie might look cool but unless you mount it right, you will knock the crap out of your shoulder. Plus your girlfriend might be too scared to shoot it, which would be a bummer if you are trying to get her into shooting. The Bushmaster, while loud, has a low recoil impulse and is accurate enough to tear the heck out of targets a good distance away.
The shottie is probably a more serious tool for you, up close and personal. Might not be fun for target shooting, but clay pigeons would be fun...
The bushmaster is no doubt also a serious tool but also more versatile in the sense that you can defend a barricaded position almost as well (it's the tactics not the tools anyway) but you can hit nicely out to 2-300 yards with lower recoil.
I'm strapped for cash so I had to choose one rifle for the time being. Well, my girl forced me into an AK which makes sense because we live in the dusty desert. If I could save up, I would love to have an M1A, but alas, I'll probably settle for the AR next.
Bottom line is they are two very different tools for different jobs. An AR can do better at short ranges than a shotgun can at longranges (*IMO* of course... a rifle bbld shotgun with sabots can do well).
A search on AR15.com or thefiringline.com might help lots.