Your thought process is good TrainChaser. You are doing it right by not getting the handgun then. I commend you for that.
For Shotguns, an 18.5" barrel is the shortest you may have by Federal Law (without a special permit). If you walked into a gun store and asked for a "home defense" shotgun, you would likely be handed a shotgun with an 18.5 inch barrel on it (they are detachable and replaceable by the way). If you asked for a hunting shotgun, you would likely get one with a 26 inch barrel (better for hitting birds in flight at greater distances). You let the person know what your gun is to be used for and they will direct you accordingly.
If you are seriously shopping around, some of the most popular pump-action shotguns are the Mosberg 500 and the Remington 870. You will not go wrong with either and they will be available everywhere you go, including your local Walmart. Mosberg has a cheaper version of the 500, I own one, called the Maverick Series. Mine is a Maverick 88 and shares attachments and many parts with the 500. It costs about $100 less and may be worth the savings since you do not plan to use it regularly.
I would recommend getting a feel for the weight of a shotgun before buying one. You can find them under $200 but they tend to be very heavy ones (12+ pounds). My Mav 88 is something close to 7lbs and gets heavy real fast. Imagine failing to be able to hold up your shotgun if a bad guy was threatening you... not good. Light is good, so get a lighter one.
Then there is the "gauge". For the standard gauges; 12 gauge is the norm that you hear, it has a pretty big kick when you shoot. 20 gauge is the next step down, and 410 gauge is the smallest. Basic "bird" or "target" shells in each are easy to find and are cheap, even at your local Walmart, but for defense shells you may want to go with the 12 gauge as it will have more variety. "Bird" shot are dozens of tiny lead pellets that will take down a bird and not much more. 00-buck (double ought buckshot) is the standard. Inside each shell is 9 (usually) pellets the size of 9mm handgun bullets, great against badguys, with explode a bird, and will anger a bear. "Slugs" are a single large lead pellet that will penatrate a car's engine, and stop a bigass bear too. They do have a hybrid (my favorite) that has both a single smaller slug and a few large pellets for a mix of the 00-buck and slug capabilities. I like those for multi-purpose defense rounds.
It will be perfectly legal to transport the shotgun across state lines... as long as it is unloaded. You must keep it unloaded in your vehicle, which means it is not so great of a defense *in a hurry*. Keep your shells nearby the gun, and learn how to load it quickly (even under stress). DO... and I mean this... DO get out and use it from time to time, even if it is only a few shots when you are camped out in the middle of nowhere. You will be more dangerous to yourself if you never practice with it. That guy will need cleaning regularly (monthly, quarterly at least) so learn to clean it. Shotguns are not the easiest guns to put back together, so if you need help go into a local gun shop and ask (go in without the gun first, ask, then bring it in). They will help.
Lastly, take yourself a hunter safety course at the very least. They are usually offered FOR FREE at your local sporting good stores (Cabellas, JAX, etc) and will teach you the basics of gun-safety and additional legalities.