I keep a folder that I give a specific name to on my C: drive. Within that folder, I have a file structure that includes things like Images, Funnies, Research, etc- all the files that I care about. I also have folders that include the entire contents of software CDs that I have loaded on the computer.
I can back this folder up monthly by copying it to an external hard drive. The external drive is a USB device and is easily recognized by both my computer and my partner's computer. We each have a folder and we both use the device for back up.
If you want to carry a program over to the new computer, you will want to install from CD. Your new system will come with an operating system and will likely have the drivers you need for the unit itself but you will have to re-install your printer drivers, office productivity software and games.
You will want to be careful here- you likely use XP today but any computer you purchase from a consumer outlet is likely to have Vista. You may have compatibility problems with your older stuff. You can order business class computers with XP still and that may be a better way for you to go.
Any additional questions, just ask.
Good luck!