unless you plan on being on the shooting range a lot I think the 'shotgun' is your best bet for home defense. Even IF you plan on getting efficient with a handgun I'd say a shotgun for home defense. You won't miss.
As for handguns.... man do you have your work cut out for you.
Are you thinking of concealed carry? If so you'll have to take that into consideration. If it's only for home then I'd get a full sized for sure.... you can get a more powerful handgun yet still have manageable recoil for acquiring the target and a second, third.... shot.
The brands I hear touted the most are Sig Sauer, Glock, and the new(er) Springfield XD is getting rave reviews. The one I carry, the S&W Shield is probably the most popular CC Handgun out there right now. I have a .40 Caliber but I'd be ok with a 9mm.
The options are endless. Revolver vs Semi-Auto - (they both have benefits), manual safety or not... most do not these days but if you're new to this I'd recommend it... NOT so much because they're safer but rather YOUR peace of mind. Type of trigger action... the options are pretty much endless.
But probably the most important factor, trumping all the rest, is how it feels to YOU. Definitely hold it, shoot it, before you buy it.