I'd recommend VNC too as:
-its cross platform
Not really a concern for one PC, though?
Unless VNC has changed since I last looked at it or I'm misremembering, I don't think it has the ability to negotiate a hardware firewall in your average home router. You'd have to open the ports manually.
I use LogMeIn and TeamViewer a lot. I've found TeamViewer to be best for one-off connections as it's simple, you don't need the remote end to start creating accounts or worrying about login details, they just click a link and read a couple of numbers to you.
LogMeIn is stronger when there's a number of techs needing to connect to multiple machines regularly. Log in to the website and get a list of all your available connections along with a live status of whether they're live or not.
In the OP's case, I think TeamViewer is going to be the best choice. You've got the option of running it as a service so it's always on, but I prefer to have it as a manual service started by the user when they need help. It's more secure that way, and it prevents you from getting the blame when something mysteriously goes wrong in the night.