You can install whichever edition you prefer, of course you'll need to buy a genuine copy first.
If you want to stick to ultimate, just buy a copy of ultimate and change the product key to the new, genuine one. Product Key Number - Change
If you want to switch to home premium, there are 2 options- you can clean install home premium, this will wipe your C: drive OR you can in-place downgrade to home premium with a well known and working hack. Of course if you had home premium originally installed, you would already have a product key (retail or OEM) that you can use. In fact if your computer came with home premium preloaded and activated you can just run the factory restore and you'll be back to factory default state. Hack to In-Place “Downgrade” from Windows 7 Ultimate or Professional to Less Premium Editions « My Digital Life
Regarding what type of license to buy, Upgrade is cheap if you have one computer. If you have 2 or more then the home premium family back is a good deal.