|I seem to recall Team Viewer does require either someone present to set up (receive/acknowledge) an access request/key; although possibly one could find a way to ensure it stay "up" once you have set that working and are then "way" from the PC.|
I have used Team Viewer for on-line Tech Support (QNAPS in my case) - and it/they was/were excellent.
However I would be inclined to consider clive_pearce's suggestion re acquiring a small NAS.. I have a three year old (at least ) QNAPS; and it works fine. It can be configured for remote access (free). Western Digital and others have similar products and options - but I think WD actually charge for remote access facility?
The minimum NAS to consider as mirrored system (has two hard drives that hold identical information); as they are easily rebuilt if per chance one drive does malfunction. If you go the NAS route anon - remember that it too is best and regularly backed up to a separate hard drive; as even an NAS can go down... And while you're awaiting the rebuild/recovery of your mirrored NAS system, you can always use the backup; and if needs-be even rebuild/restore the NAS completely from the backup HD.