The easiest way to connect to any remote linux box is through ssh. There is a freeware windows program named putty, which is a ssh for windows client. It is a tiny 400 Kb download for windows XP. it is text only.
You will need to configure your router to forward port 22 from the WAN to port 22 on the private IP of your slack box. If you haven't already, you should configure the DHCP on the router to always give your slack box the same address. Then you'll also need to know the public IP address of your connection. You can either just try to remember it, or use a free client like http://dyndns.org
to always connect to your machine through a name, as opposed to a number.
Trying to get a graphics enable connection is tougher, and a poor choice IMHO. Graphical interfaces are great for searching the web, and that's about it. All linux servers should be connected through ssh, text only.