You could theoretically own a Kindle and never connect it to a computer. You can browse various titles, read about books you might be interested in and purchase them from the Kindle Store with your Kindle via Amazon's Whispernet service. If you haven't explored this option before, press the Menu button on your Kindle, glance up toward the top right of the Home screen to make sure the words Shop in Kindle Store are underlined (selected), then press in on the center button of your 5-way navigation. You will love poking around in this area!
Be sure to let your Kindle have a close association with your computer. With just a few computer skills you can find books elsewhere on the Internet, free books even. There are certainly plenty out there, from many different sources. Once you find them, you can download them and store them in a special ebook folder on your computer for use on your Kindle. It is a terrific partnership. In the case of books, free does not mean inferior (think Classics).
With a computer, you can also visit your Amazon account, specifically the Manage Your Kindle area, and send your Kindle books you have purchased to other devices on your account, even delete one for good if you truly no longer want it. If you remove a book you have purchased from Amazon from your Kindle, it is still going to be stored in the Archives (your library) on Amazon.com. You can dig it up and have it sent back to your Kindle any time you want. In order to really remove it completely (you would actually have to purchase it again if you wanted it back), you need to delete it yourself from the Archives on Amazon in the Manage Your Kindle part of your account.