I will second what pljvaldez said. Any of the major distros should do what you want.
I started with Slackware, learned how to do what I wanted to do with it, and it's still my favorite.
I also have a laptop and netbook with factory Ubuntu that both work just fine.
I ran Debian for a while and really liked it, plus I've distro-hopped Suse, Mandriva, CentOS, and some others--I did like CentOS. Suse and Mandriva, not so much, but it really is a matter of personal taste--all the distros did everything I asked them to do.
The task that I personally found most difficult was getting Samba to work for me as a file server for Windows, because Samba is so big and offers so many options. Samba by Example
guided me to success. When I got a samba configuration file that worked for me, I saved it in four different places and have recycled it ever since.