Kev Kev
First thing I would do is get familiar with your state laws.
Second thing I would do is look for a good range where you can try a few guns out.
Personally I think shotguns get talked up too much for home defense. In my opinion they are long, cumbersome, and typically have a limited capacity. Depending on how narrow your hallways, doors etc are it could be a chore to move through your house should you ever unfortunately be in that situation. Also too big to be stored in a nightstand. For that reason I think a handgun with a rail for a light is most appropriate. I personally would recommend something mid to full size like a Glock 19, Beretta 92A1, S&W M&P, or HK VP9.
Edit: wanted to add I would try out both some handguns and shotguns. If you decide a shotgun makes the most sense for you (and it might!) then there are bunch of affordable options there as well.