What you lose with Vista, 7 and anything later is hardware DirectSound 3D support. This means, every hardware-specific feature used by a sound card (EAX, A3D, surround sound, etc.) will not work in anything newer than XP unless the game uses OpenAL natively (not common) or you can get one of the 3rd party utilities to work that brings back hardware sound (by translating DS3D to OpenAL I believe), but these are generally a bit of a hack job and don't always work. Granted, the golden-era of 3D sound was before XP even existed, so the most interesting cards and sound features would be better suited for a fast Windows 98 system. Still, many games would only provide the most basic stereo sound without hardware 3D support, so you would get no surround sound or anything else in Vista or later.
This is probably the biggest down side to using anything newer than XP for XP-era gaming.
Also, if you want to maintain 16bit executable support, for the odd situation where you might have a DOS-based application to run for an older game (or you just want to run an old game on your faster computer), you will need a 32bit OS. Using a 32bit version of Windows 7 is possible, but XP is a lighter operating system and less likely to have unfixable problems with older applications.
Personally, I think that having a computer running XP with the best specs possible is a great way to fill in the 2000-2006~ gap. Anything newer than that will run fine on any recent system. Specs that I'd look for would be:
*Very fast single and dual core CPU performance... Core 2 would be the minimum, with Sandy Bridge being about as much as you'd ever need for the most CPU intensive games.
*PCI slot(s) for running a nice old XP era sound card, like an X-Fi or some other popular card with decent XP drivers, OpenAL, DS3D, EAX and game support. There are lots of PCI-E models out there too but you have to watch out for some newer models that don't have XP drivers.
*An overpowered graphics card with good XP drivers. The latest Nvidia cards that you can find XP drivers for would be the Maxwell GTX 960, 970, 980 and 980 Ti series. Fermi (GTX 4xx and 5xx) or Kepler (6xx and 7xx) should be plenty, but the faster it is, the higher resolution and anti-aliasing you'll be able to use. The vast majority of games will have no compatibility problems with this kind of setup... anything that does is probably going to work better on a fast Windows 98 machine instead.
Now for some blitting from the back buffer.