Welcome aboard.
A shotgun is a pretty good choice for home defense. It's fairly easy to operate and you don't have to be super accurate to be effective.
Shortly after I got married some guy started calling the house harrassing my wife while I was at work. I worked on Charleston AFB and we lived on College Park Rd in Ladson. I got my wife a shotgun and trained her how to use it.
One factor in choosing a shotgun is
your size. My wife isn't very big, so a full-sized 12 gauge would have been hard for her to handle. We settled on a 20 gauge (smaller round, lighter gun). Last month I bought her a handgun, and she'll be signing up for a CWP class soon.
Handguns are good, but they take more training and practice to use effectively. If you can put the time into becoming proficient with one, you can carry it in the console or glovebox of your car without a permit.
Another point to consider is the responsibility and maturity level of your child. Will they have access to it? If you aren't planning on a safe to keep the gun in, use a trigger lock to secure it whenever you're not home. If you use a lock, take a few seconds to unlock it when you get home. It's hard to concentrate on unlocking it while your door is being kicked in.
Trader World on Cross County Rd has an indoor range. It's $7 to shoot in there. They have rental guns, which would of course be more $$. ATP gun shop in Goose Creek also has an indoor range ($5 to shoot a handgun, $10 to shoot a rifle or shotgun, or $100 for a one-year membership with unlimited shooting). ATP also has rentals.
There are several members here in the Charleston area. I'm in Summerville. I'm sure that we can get you hooked up with some advice and training.