Which ever version you like. If you want an easier to use / install etc. Try something like Fedora Core.
.tar.gz everything supports, all that is, is a compressed file. A tar file which has been compressed with gzip. All distros support that. If you are downloading programs in that format, you'll probably find that it is source code for the programs. You'll need to have gcc installed to compile them. Which again all distros will have.
You can run wireless no problems with linux, and Fedora Core if you choose that way.
I don't understand what 'freebie' software you are after? Most distros come with pretty much all of the server services you would need?
EDIT - Sorry he got in first