Hi
I think most people approach learning in their own way, however reading and playing are the best way to learn for me.
Get yourself the specific type of unix they are requesting and play with it while reading your books. If you can't find or get within the timeframe the system, get something like linux to work with.
I think the very act of installing and getting to work on the network will be worthwhile in learning about unix.
You have a limited time it seems but I think you should be fine for all the basics.
Thanks
ps. I am new to this forum as well, after searching around the forum there is an actual area that may be of use to you.
http://www.unix.com/im-new-unix-books-should-i-read/