2000, XP, Vista and 7 are all built on the NT platform. This is to say that they are not DOS based OSes. 2000 Pro was always intended to be the business workstation portion of the 2000 series. There was a Home version, Beta named Neptune, though it was never released. Microsoft instead opted to go with ME instead, for home users. This was sort of a DOS and NT hybrid, for that it did have a native DOS mode option. Also I belive it would not run on top of DOS. Needless to say it was not very accepted and had many many problem. XP was the first fully NT based OS with a home user solution. XP Home was a stripped down version of Pro, and some people say that Pro is a striped down version of Server 2003. I don't go for that idea, considering that Server 2003 has an upgraded kernel. Untill the release of SP2, there was not alot of difference between 2000 and XP, as far as the user is conserned. XP was released with a built in firewall, though previously to SP2 it was not enabled by default. Also with SP2 came a crude version of System and Security, now used by Vista and 7. It had some abilities and there are some softwares like Spybot S&D that would intergrate with XPs version very well.
Also Cat, it is not so much the age of the computer that will allow you to run older windows, it has to do with the drivers. As long as you have drivers for all the devices on a brand new computer, you can still run DOS or Windows 3.11.