Okay....
This is possible using XP Pro. It's called Remote Desktop and it's really cool
It allows for one computer to completely control another computer from a remote location. Basically, you have two computers; the one controlled (called a client) and the one controlling (called a host.) It allows the host to have complete access to the client and it's resources. You can create/delete files, start programs on the client using the client resources and lots more.
The problem is your client is running 98. In order for this to work the client must run XP Pro. The host can run whatever it likes, as long as the remote desktop package is installed. (This can be downloaded from Windows Update.
I don't know if this helps or not, but it seems to fit all the criteria you mentioned. It will allow you to create a file on the host; save it to the client; start software using the client from the host; render the file using the clients resources making it your bitch
Here's a link
http://www.wown.com/j_helmig/wxprmdtp.htm
You could run VNC, tightVNC or realVNC and it would probably work well. I just figured since you're about to buy a whole new system and install XP it would be easier to upgrade to XP Pro and get all the software built in as opposed to third party.
Hope it works out for you.