You might want to ask this question down on "what should I buy?" -- it's the section for exactly what you want to know. Scroll down a bit; it's in the device section.
I wouldn't recommend a Kindle. You want to read library books -- they're often in epub format, which Kindles can't handle. The "free 3g" is only for buying books from the Kindle Store while on the go; if you're not planning to buy books while sitting on the subway, that's not something you'll want to pay for. Also, I personally find that keyboard annoying. I have no interest in typing while reading (obviously people who need to take notes, such as for class, feel otherwise).
Before I got my ebook reader, I read Project Gutenberg books on the computer. The difference is astonishing. E-ink is the best thing that ever happened to reading since the page. As one of those people with limited library space (it's at the point where the floor is at risk; when we moved, it was the books that nearly sprained P.O.D.S.'s forklift when they took our pod off the truck) being able to tuck at least some of my books into a pocket-sized dingus matters a
lot. I'd give up one of my lesser fingers before I gave up my ebook reader.
By the way, you've probably asked the wrong people whether you should get an ebook reader. Of course you should get one! If we didn't think everyone should have one, we'd probably be on some other forum.

I don't know how I ever lived without mine. Everyone should have one. Maybe more than one.
When you get yours and you're looking for free ebooks, check down in MR's own library, then try sites like Project Gutenberg, ManyBooks, Feedbooks, etc. Those are my primary sources of free public-domain books. There's also the Baen Free Library, if you like science fiction (I do). Baen also sells me a fair number of books, as does Smashwords, O'Reilly, and the occasional indie. I have a Sony Reader and I've never used the Sony store; I couldn't tell you how. There are too many other places to get books -- great books -- that don't involve me signing my soul over to a vendor.