Welcome to the wonderful world of stamping!
Stampers either treat their stamps like valuable treasures and clean every speck of ink off as soon as they are used, or they treat them as tools of their craft and don't worry if the rubber is stained and the mounts are smudged with inky finger prints.
I'm compulsively clean with mine, but that's mostly because I'm a CTMH consultant and lots of hands use my stamps.
As long as the ink hasn't built up to the point that the rubber image is distorted, staining doesn't affect the image at all. Some inks, like pigment and embossing inks are so think that if they are left on a stamp and dry hard, they will build up like that. This can be taken care of with a stamp cleaner, or even a cleaner like Simple Green, but the rubber may remain a little stained if the ink has been there awhile.
Some stamps that come "unmounted" come with wood to mount them on (Stampin' Up stamps are like that). You can also buy unmounted stamps that are just sheets of rubber with images. There are a variety of ways to mount them either permantly or temporarily on wood or acrylic blocks. Since you are new to using unmounted stamps, I'd suggest you visit with the seller about exactly what is included with the rubber. It may be that they are just new Stampin' Up stamps that need to be mounted on the wood that is provided with the stamps.
If you have any questions after you find out whether mounts are provided, post again, or e-mail me and I'd be glad to help.
Have fun!