The different versions have different features unlocked. They're all the same OS though and each has the exact same performance.
For a home computer, Home Premium is fine, Professional is for business computers, it has the ability to join a domain and stuff like that, and Ultimate has everything unlocked so it's the most expensive but not really what a home user might need.
Here's the problem. As technology advances, old tech is phased out. So the technology your old programs and hardware relied on will eventually be phased out for newer, better tech. This same thing happens with operating systems too. Even if you installed Windows 7 that doesn't mean it will work with your new hardware.
The best thing to do is keep your old computers around so you can run your old software. Another solution is to install your old operating system and programs into virtual machine. When you need to use those old programs and hardware, spin up your VM with your old OS on it and get work. It's actually pretty neat in that its portable. You can save your VM file to an external hard drive and take it from computer to computer. All you need is to install the VM software on the computer and you're good to go.