welcome to LQ.
I have tinkered with some Linux stuff in the past, however I have received notice that Ubuntu offers a greater experience and I can accomplish greater things with the Ubuntu system than any other.
Wow, that sounds like marketing speak. Were you lunching with people from Canonical? Ubuntu is just another GNU/Linux distro. Ubuntu won't enable you to "accomplish greater things" than most other distros. Don't get me wrong, Ubuntu is a perfectly fine distro, but it's nothing magical.
I would like to know what the best steps to take to accomplish this and what are the best options for a pc brand to use.
Any distro can run a samba server and act as a nas. Just install the os then install samba. To give more specific advice you'll need to tell us your requirements. Eg how much disk space do you want? Do you want raid? Does the diskspace need to be expandable (eg using lvm)? What do you actually want to use this nas for? And so on. PC brand is not so important, PC specs may be. But again it depends on what you really want.
However, if you just want a dedicated nas you may be better off looking at a dedicated nas box like those made by synology (http://www.synology.com/