Logmein should be fine for what you want to do. I have it installed on families pc's and then they call up and say something not working, I connect and see what they have done. It's been free all the time I have been using it.
If you don't mind forwarding ports on your router and setting up some software to connect to, then VPN server on the box you want to control and also VNC on it (so you can see/control the screen)is a good option. As well as clients for windows, mac and linux, there is also one for android phones. So you can even control it on the go
