A real thin client has no hard drive or storage medium, and uses PXE as it's bootstrapping mechanism.
I had a big ass post to this thread and thanks to what we think is a GCC optimization bug affecting just a few applications, my web browser crashed once again.. so it is lost.
Anyhow, you want to evaluate what your limitations are first, involving network bandwidth and processor power along with memory capacity of your systems.
I for example have GigaBit ethernet on this laptop, so I wouldn't really need to evaluate much if my routing appliances and other nodes have GigaBit ethernet capabilities.
I would suggest X.org server/client setup though right off hand regardless of knowing anything about your setup. The reason for this is as stated in this posting from RealVNC's website:
http://www.realvnc.com/pipermail/vnc...er/010222.html
(Note: That is from 1999, so it's nearly a ten year old document.)
That X.org server/client architecture was built specifically for use over the network and anything that can be rendered locally, will be. VNC on the other hand will transfer all data over the link, but has the advantage that not all operating systems have an X.org implementation and is more platform independant, you stated you are using two Debian Linux systems, I would rule out VNC immediately.
FreeNX might also be something to look into as it is a free implementation of the commercially used NX server.. and is good for high latency networks using high compression for data.
Can you state more about your network, limitations and hardware you would be using?