If I understand your question correctly, you want to be able to run an X-Windows Client on your Microsoft Windows Machine. Can this be done? Yes. Can it be done for free? I am not sure. There are several X-Windows Clients out there and they do work. I used to work for Nortel and we did this all the time with HP-UX and Windows NT. We used a program called Exceed. It was NOT freeware, or GNU.
Here is a site that you may find helpful
Here are some others you may want to check out. Far as I can tell most of them run about $100.
Now, if you are looking for a free option to manage and do stuff across a network connection , and for this I suggest at least 10/100, you can use something called VNC. Its not super fast, but it works, and its free. The cool thing is its Cross Platform capable. This means you can do the same thing on Linux, IE have a box with your windows desktop up on the screen. I suggest a varant of VNC called tight VNC.
Now, for the other part of the question, 6.2 should work fine. I have never setup any of the Payware so I am not sure, but each should have detailed instructions. You might want to do some reading about xhosts, check the man page on that command. xhosts usually is used when setting the system to export a display out to another box. With most or all of this you will need to make sure your windows box can see the Linux system and has permission to access what it needs.
I hope that was not to basic or word filled.
I am sure other folks might have stuff to add, and by all means correct me where I am wrong ;-)