That would be completely up to you.
That would be your best reference, virtually every single distribution is listed on that site. You will need to do your research and download which one would fit your needs. I can not really suggest a distro for you because what I do and what you do are two completely different things. I am more of a developer, therefore I use more bleeding edge and development software. I mainly use Fedora and OpenBSD, yet for you, it could be something else.
As far as not burning to a disc, how else are you planning on installing?