As for caliber, I prefer .30-06 because of its versatility. You can go up to Maine and hunt moose, hunt black bear locally or go out west for elk or antelope, and the ,30-06 will do everything you need it to do. It can stabilize heavier bullets and will give a flatter trajectory than the .308, especially if you handload. But if you do not envision ever hunting anything bigger or more dangerous than a whitetail, then a .308 will fill your needs just fine.
If you are putting more of an emphasis on self defense than hunting, then a Remington slide-action rifle like the Remington 760 may be a better choice. You sacrifice some accuracy and reliability, but you can get ten-round aftermarket magazines that give you some pretty good firepower. A 760 in .308 would not be a bad choice.
So my advice is use the 870 as your primary self-defense tool, and get a Savage 110 in .30-06 as your hunting rifle and long-range defense rifle. I recommend the Bushnell Elite 3200 3-9x scope. It is an excellent buy, and the Elite series are far superior to previous Bushnell offerings; damn close to Leupold in quality at a far, far lower price. I think this will give you the best value for your money, and the most flexibility.
ping
You make a good point about the scope. It is a critical part of the package. I would opt for nothing less than a Leupold Vari-x II. I generally figure the scope should cost nearly the same as the rifle.
I have a hard time recommending the Savage as an all around rifle. The are bargain priced, very accurate, and have a nice trigger, but, my brother has several and says that he would never use them for serious hunting for trophies or dangerous game. He has simply had too many reliability problems with feeding. He is a certified armorer and firearms instructor and a pretty good semi-pro gunsmith, so I take his advice seriously. This is why I recommended the Ruger. There are lots of good guns out there, but as I do not know NewJersey_Joe’s experience level, I hesitate to recommend a used rifle. There are often bargains after deer season, as has been mentioned. If he is willing to get into reloading, almost any relatively modern deer caliber or better could be made to work.