Welcome to THR, ACbutch. Sorry to hear things are not going so good in your neighborhood. Thinking about a shotgun is a reasonable response to news of unwelcome visitors in the middle of the night.
But just buying a shotgun won't help a lot though, if you don't learn to shoot it effectively. If by 'hand held' you mean a shotgun with a pistol grip only rear stock, that's a tough approach to take if you're just learning to shoot shotguns. Best bet by far is to stick with a conventional type shoulder stock, and learn to shoot that configuration. Then you can start experimenting with other options and see if you can do better than with a conventional gun. Chances are, the pistol grip stock will hurt more than it helps.
You will want to be careful not to get a shotgun that is TOO light. Remember, the rules of physics still apply, and the lighter a gun is the more it is going to belt you back when you shoot it. I would suggest you start with an 18- 20" barreled repeating shotgun, pump action, in standard 'riot gun' configuration, from one of the major American manufacturers- Remington, Mossberg, Ithaca or FN/Winchester. As long as you have no physical disabilities you should be able to handle such a gun, and it should not be a problem to shoot if it is properly fitted to you. Most of the time that means making sure the stock is the right length. New shotguns are often like new pants- they are too long and need to be shortened a bit.
Deciding on a gun is far less a problem than the process of learning to shoot it. Any good pumpgun will work fine, if you do your part. Remington supplies most (about 90%) of the law enforcement shotguns in the country by far, and the Remington 870 has been around since about 1950- there are millions and millions of them in circulation. It happens to be my favorite, I've been shooting them for about four decades now.
A lot of folks like Mossbergs too. They're good guns, a little lighter in weight since they have an aluminum receiver instead of the steel receiver of the 870. Mossberg's Model 500 is more often seen, the military contract Model 590 is IMHO a better design, since it's easier to clean the tubular magazine on the 590.
Ithaca's Model 37/Model 87 has been in and out of production several times now. Right now the company is back in business, I hope it stays- the design is an American classic. Ithacas are all steel guns too, but they tend to be a little lighter than other all steel designs. They have a long history of solid performance in the sporting field, with law enforcement, and on the battlefield.
Winchester's Model 1300 went away when the company closed its doors recently, however the same design is still in production as the FN Police Pump Shotgun. It's an aluminum-receiver gun, out of the box it has a lot of features that make it appealing as a defensive shotgun- an 18" barrel with rifle sights, interchangeable choke tubes, a shortened stock with a recoil pad, and a durable finish.
It would be hard to go wrong with any of the above, the big thing is to learn how to use whatever you get effectively. A shotgun is not some sort of magical talisman that will keep evil at bay by its mere presence. It is up to the shooter to do that if necessary. But that comes after you get the gun.
My advice is to find a friend or relative who knows shotguns and let them teach you the basics, then get some hands-on experience with different makes/models. It's easier to make an informed decision after you get some trigger time on different guns. It may take some looking on your part to find someone helpful, check around at different sporting goods stores and gun clubs too while you are looking for beginner level help.
Check with the NRA to see if anyone near you is offering classes (
http://www.nrahq.org/education/training/basictraining.asp ). See if there are hunter safety classes available near you- you may have no interest in hunting, but the class will give you a good grounding in gun safety. You will have to be proactive in getting started, as much as I hate to say it far too few people will really go out of their way to help a new shooter get started.
I wish you good luck in the process, don't be shy about coming back here if we can help from the other side of your monitor.
Stay safe,
lpl/nc