Isis -
20 squares @ 4 x 4 end up being almost 1/4 yard. You can buy a fat quarter for $1 if you get a good price, and around here they typically run $2 in the quilt shops. If there is any way you can set up a cutting board, you will probably get better prices by cutting your own squares.
The charm packs are great because they are usually pre-coordinated. Nothing wrong with using that convenience, especially since in your situation the extra $ spent may be less important than the space constraints.
I think if you choose the charm pack route, you can make a beautiful quilt. I've seen lots of packages on the web and in shops that would make pretty quilts. You will still have to do some cutting, though. If you start with the squares, you won't have to have much space - a TV tray as some others suggested will suffice.
Be sure to post pics of your finished product.
Darren