I have a little experience with shotguns. I think you are on the right path as far as the 870 goes. It is a great gun that you will enjoy shooting. Get the model that you like the best.
Don't worry too much about the stock style-fixed/folding/pistol. However, you don't want the stock to be too long.
As far as rounds go-slugs are for distances up to 150 yards and are a solid projectile. Buckshot is primarly used up to 25 yards for self-defense. Birdshot is used for hunting guns. The bigger the number the smaller the shot.
As far as capacity goes, five is plenty. An extended tube would be ok with six total rounds. That is a lot of firepower. Go out to the range and shoot a popper with a handgun and then with buckshot. You will be suprised how the buckshot knocks the popper down.
My personal defense shotgun is a 1970's 870 Police model with a 20" rifle-sighted barrel and four shot mag. I love it and wouldn't change it.