I love this site. It's not "records" such as census records or tax or wage receipts, but poetry, myths, and a few letters. It's got translations as well as transliterations if you wanna see what Sumerian "sounded" like. Very cool, in my non-professional opinion.

I'd also suggest "History Begins at Sumer" by Samuel Noah Kramer. It's older; First edition was written in '56, and I've got the third edition which was published in '81- but I still found it a great introduction.

To be honest, a lot of records are incredibly boring -- they record what goods went where and so on, or they're self-aggrandizing kings.

However, Many articles will publish various cuneiform tablets. Here are some articles that publish some that would be more interesting: c.f. Westbrook, Raymond. Old Babylonian Marriage Law. Horn, Austria: Verland Ferdinand Berger & Sohne, 1988. Print.

Figulla, H. H. and W. J. Martin. Ur Excavation Texts, vol. V, Letters and Documents of the Old Babylonian Period. London, 1953. Web.

Gadd, C. J. "Two Sketches from the Life at Ur." Iraq 25.2 (1963), 177-188. Web.

If you have a specific site you are more interested in, look for the original excavation reports or the original publishing of the texts from that site (These sources are old babylonian ur, just because that was what I had on hand) You can ILL them, but many of these books are rare/expensive and some might be hard to obtain.

For general background on the region, I would recommend Van de Meiroop's history of the ancient Near East. If you have no history in the region, this might be a better place to begin than the primary sources themselves. The other starting point you might look into is the Epic of Gilgamesh, or, as the other poster states, a mythology dictionary/guide.

Best of luck. Please let me know if there are specific sites you'd like help with or you need further help.

Thank you for all the information everyone. I've got some long nights of reading ahead of me.