Benelli Super Nova would be my first choice. Remington 870 would be my second. Not buying anything but my first or second choice would be my 3rd choice.
For upland hunting, life is pretty simple. Modified or improved choke, both of which come with the SN or 870. 6, 7 1/2, or 8 shot, depending upon how close of cover you'll be hunting - I'm almost exclusively 7 1/2.
Any American Citizen who is not prohibited from purchasing a firearm is able to purchase a long gun in any US state. You might be able to find a gunshop which offers discounts for active military. As mentioned above, you'll have to take hunter's education, then buy your license in the state you're hunting. For pheasant and quail, you should just need your license, for Dove you'll have to add your HIP stamp for migratory birds - which is very cheap (forget what it was this year?). Both the 870 and SuperNova should come with a magazine plug (likely installed) which limits the capacity to 3 rounds, in concession to migratory bird hunting compliance. This can be removed for upland game hunting. Most states will require blaze orange vest and hat for upland hunting, but you'll be instructed on that for your particular state during your Hunter Education course. Blah, blah, a million more details on nook and cranny stuff, which you'll be able to pick up from the bird dog association or your hunter's education course, so I'll leave you to learn it there...