There's plenty of excellent advice given here...
I think what's most important is after finding the firearm you feel most comfortable with is practice practice practice.
I can't tell you how many times I see Police officers come down to the range because they didn't qualify on their semi annual tests. And they're just shooting NON moving paper.
For home, I'd go with a shotgun with the shortest barrel allow by law. Maybe go with a remington 1187 (semi-automatic) or go with the forever reliable remington 870 (pump). Try shooting trap and skeet so you can get a handle on "moving" targets. Maybe go bird hunting every so often.. That'll sharpen up your skills.
If you want a handgun, I'd go with a browning hi-power, glock G18 :w or a HK model 23 :y