I was thinking that I would use a mini mac to store all my DVD on. Will it store them, so I get the same picture quality as my high quality DVD player? I have a 70" TV is this a good or bad idea?
Yes, it'll work fine and look the same as the DVDs you ripped looked on your other player... assuming your TV accepts DVI or VGA input at decent enough resolution, which it should.
You probably want to consider getting a mini-sized external hard disk to store those DVDs, by the way. It'll sit under the mini and looks pretty decent.