Hiya,
I've shouldered many a shotgun over the years, here's my 2 cents.
I would stick with a slide/pump action shotgun. My reasons for this are:
1)Autos are nice however, they are for experienced shooters and since one of your intended roles is home defense, simple is better.
2) Nothing like the sound of a pump action to strike fear into the heart of a perp, everyone on the planet knows the "shuck-shuck" sound of one being racked. You just heard it in your head didn't you?
3) Easier to load and reload, no bolt lock open to deal with, and easy to clear.
4) A pump action is far less complicated and more reliable.
I understand your reasons to go with a 20 but I would suggest you look at 12's also. 20 is slightly light for deer, you have to be right on with your shot placement and keep your yardage on the shorter side. Also, you will have less load choice in 20 than in 12. Also, your model/barrel choices are less in 20. (sweet 16 used to be very popular as a "just right" gauge but with the demise of the Winchesters and Browning Auto-5's, it has fallen in popularity)
Now as far as brands and models, any of the major brands will serve you fine, Mossberg, Remington, Winchester, Benelii, Beretta, If you want the utmost in reliability, look to the military/police models such as the Mossberg 590 Military, Remington 870 Police or the FN Herstal. All of these are built like tanks and are designed to work when others won't.
A high quality 12g pump with a improved cyl/rifled barrel with sights and a interchangeable choke barrel set would cover all your intended uses easily and reliably. I saw an example of how good a 870 can be at a steel plate shoot one day, an older trap shooter came to watch the action, the shooters there recognized him and dogged him until he went and got his 20yo 870 with a full choke brl, He ran the course as fast as any of the auto shooters and took down all the targets. The ones eager for him to shoot weren't too happy after he knocked them down a place.
Hope I have helped, feel free to PM me. I'm an NRA instructor and can give you a bunch of info.
Tom