I would not be inclined to use gotomypc.com. I think the free options are just is good if not better.

If you have XP pro, use the affore mentioned remote desktop. On your router open port 3389 and forward it to the computer with remote desktop enabled.
There are two IPs involved here, the WAN and LAN. WAN = wide area network and is the IP address you get from your connection (ISP). It is usually provided to your cable or DSL modem via a protocal called DHCP (dynamic host control protocal?). I'm not farmilliar with no-ip, but it sounds like a way to determine this address. It is, for all intents, your address to the ouside world. Its the address on your front door.
Behind the router you have LAN address, (local area network). These represent individual computers. If the WAN is your street addres, these would be rooms in your house (not visable to the outside world, but you can open a window from time to time).

If you don't have XP Pro, google for Tight VNC. Its a similar solution. you run a small server program on your home PC, open the right port (not sure what it is) and then have a client on the remote PC that you use to connect.

In all cases, from outside of your rotuer (the rest of the world) you use the WAN IP address.

Hope that is more clear than it feels like to me right now.... typed in a hurry.