Linux setup for Raid5, Remote desktop & router?

Ok, so I'll give you a quick run down of my current setup.

I currently have 1.8Ghz dual core pentium with 1GB of Ram running Windows Server 2003 that I use as my home server.
Its currently gets used as a router, sharing my cable internet across my network (I have an old cable modem thats not a router so I needed a server to share the internet for me), It also acts as a file server, where I store all my movies, tv shows, music, etc, as well as doing all my torrent downloading on it, since I leave it running 24/7. I also have remote desktop setup on it, so I can access it from anyway.

Now I'm about to upgrade the HDD's in it, and I'm going to put in 4x 1TB drives and set them up in a Raid5 array, so I atleast have some redundancy incase 1 of the drives fails. The board doesnt have hardware raid, and I'm not interested in buying a hardware raid card. So I plan to setup software raid. Now after abit of reading it seems Linux handles Raid5 arrays, and particularly software Raid5 arrays alot better than server 2003 does.

Now I have never really used Linux before, but I am open to experimentation. So I would like to know from some of the experienced Linux guys here, what would be the best Distro for replacing Server 2003, that will give me good software Raid5 performance, and will also be able to easily setup as router with DHCP to share my internet, and then does anyone know of any software for Linux which will allow for Remote Desktop style connection. Preferably so that once its setup I can easily connect to my server from anyway, without any additional software on what ever PC I'm on. So i doubt you could use the Remote Desktop Connection built into windows to connect to a linux based machine, but maybe if there is a way to setup a web-browser based connection, so it will give me my servers GUI in a browser?