I'll second the recommendation for realvnc. I used to use remote desktop connection, but now use VNC. I've found the following:
1) Only XP Pro can serve as a host for RDC. While Home edition can serve as a client to connect to an RDC, it can not accept incoming connections. RealVNC is platform independant, and can be hosted on linux, windows (any version). There's even a mac port.
2) An RDC connection will interrupt the local user's session, and lock them out of the computer for the duration of the connection, e.g. only one of you can use the computer at any given time. A VNC connection can allow both to use the desktop simultaneously (useful for collaboration).
3) Either VNC or RDC can be used outside of a LAN. For RDC, forward port 3389 in your router to the local IP of your host machine. I'm pretty sure the default port for VNC is 5901, but I believe it's configurable to whatever you like.
4) I'd definitely recommend using a VPN to connect to each other. A VPN is relatively easy to configure, and I'd be happy to send directions to anyone who'd like them on how to configure a basic VPN within windows XP. (Even XP Home can accept incoming VPN connections).
I've set up quite a few remote desktop solutions for clients at work. RDC is convenient if you'd like to access your home computer while away, but for most other purposes I'd definitely recommend VNC. The URL again is
http://www.realvnc.com.