There should be no problems with what you want to do and no extenders needed, assuming both of the following are true:
- The PC you want to view the content on can reach the network location where the programmes are recorded
- There is sufficient bandwidth between them to stream the content without buffering issues
I have a similar if opposite setup (Vista Home Premium with plasma in living room, desktop with 7 Pro in office) and can view recorded TV on the Vista machine when I'm in the office with no problems. In fact, I'm sure I even tried playing back the same programme simultaneously in both rooms and it worked fine.
Windows 7's libraries will make it a lot easier to manage this content. Either Professional or Home Premium would work fine for viewing the recorded TV, but as I recall Home Premium doesn't allow remote desktop connections so I'd go with Professional as it makes it a lot easier to administer a HTPC where you may not have a convenient mouse/keyboard set up all the time.