For an introduction to Talmud and Mishnah, I'd recommend Back to the Sources, which will also take you into later rabbinic literature. The first section of Targum and Testament is a good introduction to the Targumim. I also like Shaye Cohen's From the Maccabees to the Mishnah, which essentially does what it says on the tin. The chapter on early rabbinic Judaism is probably worth it on its own, but it also provides good introductions to much earlier Jewish texts outside the Hebrew Bible (which you don't list).
Thanks for the replies. The commentary by Rashi is too long for me. Iv'e found these 2. They both look good:
http://www.amazon.com/Back-Sources-Reading-Classic-Jewish/dp/0671605968
http://www.amazon.com/Jewish-Interpretation-Bible-Ancient-Contemporary/dp/0800697987