Aurora,
If you really want to learn Yiddish, While others might not like it, The best places to learn it are the YIVO institute (on 16th St in Manhattan) and the Folksbien which is a organization dedicated to the Yiddish theater and culture. I do belive that the YIVO gives yiddish language courses, but otherwise some universites in the NYC area also give them.
These organizations are not really interested in the religious aspect of Yiddish, just in the preservation of the language and culture.But I have heard people from the Folksbien speak yiddish with the proper accent exactly as my grandmothers spoke it.
You probably would be more interested in reading the works of Shalom Alechim (Tevye the Milkman (Fiddler on the Roof)) , Issacs Bashevets Singer (Yentel). Perhaps you could read Tevye the Milkman in both Yiddish and English and get a good idea of the words, If you have a knack for Languages you should be able to pick it up that way. A True Torah book might not be the best way to learn as many are intricate and complicated and you might need to know much more backround to really get it without being bored.
Be advised that many secular Yiddishists tried to change the Yiddish alphabet from Hebraic to Latin. So you might want to take some Hebrew courses to learn the proper Hebrew Alphabet and then get the yiddish sounding equivilant (It is similar although not exact)