the only thing i think u'll need is graphic libraries (jpg, png, tiff, ...)
the best way to find out is to do an LFS system (u could also go with a very basic install of a distro but with LFS u'll learn more), install X on it, and then just install blackbox on it
run configure for blackbox and it should tell u what extra libraries u still need. every required library should be mentioned in the README from the blackbox tarball, or listed on their site. then just install each library at a time, untill the blackbox configure doesn't bitch anymore and the compilation finishes succesfully.
but i would definitely go with an LFS system since u want the system to take up as little space as possible. with LFS u get a very, very basic system and then u'll only install what u need, nothing extra