I agree with the vast majority that if you focus on just one Chinese language, it should be Mandarin, which is the same as “pu tong hua” that was also mentioned. The thing is no matter where you go you will be able to speak Mandarin, and make yourself understood, although you might not be able to understand everything that others are saying. The exception that was already mentioned is Hong Kong, and some parts of the south, particularly in Guangdong province (which is the province that borders Hong Kong), where Cantonese is primarily spoken.

In both Beijing and Shanghai, Mandarin will be fine, although Shanghai does have it’s own dialect that is quite different from Pu tong hua. I had a friend demonstrate a simple sentence for me one time, which I could understand in Mandarin, but had no idea in Shanghaiese (or Shanghai hua, as they would say in Mandarin).

If you end up being assigned to some other city, post another question and there is probably someone who can tell you what other primary languages are spoken in that region. For instance in parts of the Northeast, Korean is spoken almost as much as Mandarin.

One resource I found helpful for language learning was Rosetta Stone, but it’s not free. Didn’t teach me a lot of every day expressions (that doesn’t come until the higher lessons), but I found myself thinking in Chinese the quickest using that method. I probably shouldn’t even be mentioning it because it’s not cheap and you did imply “free”, but I think it’s a good enough resource to mention anyway.

Also, try going to Zhongwen.com. That site may not be very basic for a beginning student, but they do have links to a lot of other sites some of which might be helpful to you.

However, that being said I do agree with the poster who said that you should consider learning Mandarin for the long haul. These resources can give you a jump start, but you really need a person. There are some aspects of learning Mandarin that really need a native speaker to correct your pronunciation. Use whatever resources you can until you go, but when you get there see about getting a tutor. For that I recommend the book: The Whole World Guide to Language Learning available at Intercultural Press. This book will give you a lot of hints for taking control of your language learning and working with a tutor.