Carefully Faded, I bet you have a Simmons Beauty Rest - the Bowling Ball Bed - the "do not disturb" bed.
We bought one about 4 years ago. I don't sleep well, and any disturbance can keep me awake for hours. Kev or I can toss and turn, and no disburbance, unless one of us whacks the other. I absolutely love it! It is firm. And we rotate it about every 6 months for wear, too. No flip I like too.
Else, if you sleep with someone else and motion is an issue, I highly recommend this mattress.
Box springs these days are usually only boxes. Platforms for the mattress to sit on. If your box spring is just a box, no you do not need to purchase another. Just a sales ploy (read lie). Unless, of course, you want your fabric to match on the box and mattress.
Pillow topper mattresses, IMHO, are a waste of money when you can buy a separate pillow top for far less money (Costco has the tempurpedic-type foam topper 2-1/2" thick for $119 queen size). It's usually the pillow top that wears out before the mattress support.
Price 'em. You'll find a vast difference in prices for the same basic mattress with different custom store names. With a custom in-store name, they don't have to give you a better price for a "comparable" mattress because it has a different name. Another marketing ploy (read lie).
Good shopping. Don't forget to try them out in the store.