Not sure really without digging on hardware but if you want to approach 2013 you'll need something that runs XP with it's final service pack to ensure you can still throw almost any Win9X/DOS level stuff at it along with the modern 2013 releases you'd care to mess with. Once Vista/64bit anything rolled out stuff, even MS's stuff like Age of Empires 2 rolled over and died pretty badly which was annoying along with anything 16bit installer based (original Civ and Sim City for Windows for example.)

Hardware I'd probably try and figure out what the best thing in 2013 you'd want to play at a medium level and work back from there. The faster and beefier you get on hardware the harder time you'll have with the 90s and earlier-mid 00s stuff running right if at all. Like for instance I'd probably look no better at an old quad-core or dual core intel CPU stuff if that, again depending on what you want. Your problem here is you're looking at such a wide range of years you're asking for trouble since there isn't a DOSBox type catch-all for Windows stuff for so many years which GoG.COM heavily relies upon along with working with the old developers or their own coders to bring stuff back to life so it runs right (and maintains it.) You'll be stuck doing that foot work.

If you want to toss something like Witcher 3 in there, you can forget it. The horsepower needed for that game is crazy if you want it to be like back of the box quality or even semi-respectable.

My suggestion perhaps find a cut off point, make two machines but hopefully have the ports (monitor, audio, mouse, keys) interchangeable so you just have to swap between the cases. I haven't dug quite the way you have but I've been beating around the idea of a pre21st century computer since the old stuff isn't so happy on the newer, a win98se centric device so USB isn't out of play. But that's before what you want. You're asking kind of the impossible because on one box you're asking to have 64bit only apps and 32bit and 16bit all run, that's a stretch.