You have several choices but I would assume you have a good reliable connection to your home computer at decent speeds, especially if you want to do graphical presentation. Most Cable/DSL modems do not have stellar "upstream" capabilities. They may have 1.5Mbps downstream but upstream is usually limited to 128k or 256k max. Even then there are many possible choke points between your home machine and your school's machine.
Having said the above, a 14.4k modem connection is *more* than enough if you don't intend on doing any remote graphical work and only use command line stuff. You would use ssh for this (get putty.exe from
http://www.openssh.org/ for the windows machine you want to access from).
For graphical work the easiest thing that you probably do is turn on the VNC server on your Linux box. You can vnc into your machine and get a remote desktop. I personally do not like VNC to remote control an X session but it will work. Another option is to install Cygwin with the win version of XFree on the Win box. You can then turn on XDMCP on your Linux box and get a graphical X login on your desktop at home just as if you were there and you can log in and get the same desktop that you get when you log in to GDM on your machine locally at home. The Cygwin method is more difficult because it requires the installation of more software on the Win client and some slight configuration of that software.
Do you need graphical access? That is, is the app you are creating a graphical app? If it is not, everything can be done easily from the command line through ssh. Why don't you just ask your teacher if you can wipe that filthy Windows off of one of the machines and install Linux?
Also with Cygwin you can run most of the GNU apps (gcc etc) right on the Win box. See
http://www.cygwin.com/[ October 23, 2002: Message edited by: void main ]