Why not just use Terminal Services? It is built into Windows XP Pro and is much faster than the competitors you have mentioned. Ok, if you are accessing your PC at home it will not be so easy. You could however, with relative ease get a static IP address and configure security and/or VPN to allow access to your PC at home. As mentioned at WOL (wake on lan) card would also allow you to remotely power your PC on and off (although take care and get a well reviewed card).
Try to use pc file transfer. It is easy to set up, affordable, reliable, there is no timeout, you can keep connected as long as you want. And it's cheaper than Logmein. PC File Transfer costs for $29.95.