Agree with borgie on going with a faster machine. Something to point out: the Fallout and Command & Conquer games have been re-released (they are not "remasters") by Interplay and EA respectively, and will run fine under XP, 7x64, etc. You do not need a "retro machine" for them. I'm not as familiar with the rest. For C&C I'd suggest Command & Conquer X: The First Decade, and Command & Patch if you need to run it under 7x64 (should work on 8x64 too). For Fallout, get the Interplay "Fallout Trilogy" package (it includes some community patches/mods on the disc as well).
Overall I would agree with the idea of a fast Pentium II or a Pentium III, and a decent graphics card (even if you don't need 3D acceleration, there's no reason to avoid something like GeForce - the prices are going to be equally low and it gives you many more features). If you need a machine that can be slowed down dramatically for whatever reason, I remember reading about some Dell OEM P2/3 era machines that have that capability - I forget which specific models were included though.
EDIT:
Just spyed this thread about TIE Fighter and X-Wing:
X-Wing/TIE Fighter re-release
IMHO would be worth looking into. That just leaves X-Com, WarCraft, and the LA games to investigate - a bit of web searching indicates the Battle.net Edition of WarCraft II is a good candidate for a newer machine, so that just leaves WarCraft 1, whichever version(s) of X-Com you'd like to play, and the LA games. It looks like WarCraft I is a DOSBox candidate, so that leaves X-Com and LA.