A. Free is good, I always think.
On this link you can pick up Konrad Volk's 'Sumerian Reader' : http://www.scribd.com/doc/49435588/A-Sumerian-Reader-K-Volk
and here, Daniel A. Foxvog's 'Sumerian Grammar' http://home.comcast.net/~foxvog/Grammar.pdf

For somebody starting from scratch, Wikibooks provide lessons in Sumerian, here: http://en.wikibooks.org/wiki/Sumerian.
The intro is totally brilliant, and the lessons themselves start here: http://en.wikibooks.org/wiki/Sumerian/Grammar


Indeed, free is nice, and Internet-resources are sometimes even more up-to-date than books! :-)

Just recently I came across the work and website of John A. Halloran:
For a book review of his lexicon (free e-version: http://www.sumerian.org/sumerian.pdf ), see: http://www.bookreviews.org/pdf/5622_5939.pdf

Daniel A Foxvog's grammar is also here: http://www.anelanguages.com/SumerianGrammarFoxvog.pdf
with glossary: http://www.anelanguages.com/SumerianGlossaryFoxvog.pdf

I haven't checked this one myself yet, but possibly useful (may refer to either Sumerian or Akkadian): http://www.helsinki.fi/~whiting/intbab.html