Pentium Dual-Core E6500 (2,93 GHz), 2GB DDR2-800 RAM, some ASRock board based on i965 chipset, a ATI Radeon HD4350 (passive!) and some harddisk (depends on how many capacity you need).
This combo is pretty cheap, quiet (only two fans, one on the cpu, and one inside the power supply) and should be fast enough for pretty much every classic out there.
Those Atom based stuff is fast enough for the classics, however I wouldn't go that way as you never know what comes up next in terms of emulation.