I asked a dealer at a computer show about the Cyrix chips that are on those mini-ITX mainboards. He stated that the benchmarks posted on the net about the performance of those chips are B.S. He said that the Cyrix-1000mhz performs worse than the AMD K6-2 series (and implied that the site that did the benchmarking must have been sponsored by VIA because it doesn't touch the Celeron-666 in performance that the site said it was the equivalent of).
So, as for the Cyrix chips - I'd avoid any solution based on that chip like the plague.
As for noise levels - Antec sells a PSU called "TruPower" that has integrated thermally controlled fan levels. In addition, it has fan PSU lines to drive up to 3 external fans - all automatically speed controlled by the PSU. Just hooking my case fans up to this PSU easily cut the noise level emitted by my case in half. Another thing you can do is choose a lower-rpm CPU fan. Its especialy worth it if you have one of those 7200rpm screamers on your heatsink already.
As usual - fans are typically the loudest source of noise. If your current video card has a fan, try a Geforce4MX (no fan on most of these units). A lot of mainboards nowadays come with a fan on the North Bridge - if it has a fan than it almost certainly needs it, so no choice except to change mainboards there.
Finally, CDROM drives typically make one hell of a whine when they spin up. At this point in time the only option to fix that is to get a Kenwood TrueX drive, but it may not be worth it if you use CD-R's or CD-RW's or rip audio. But if you do none of these 3 things, the Kenwood is certainly right up your alley.
As for what I'd recommend for you -
Mini-tower case w/ Antec Trupower PSU (330w)
Kenwood TrueX CDROM 72X
Some flavor of Socket 478 Celeron or Pentium4
This setup should be relatively quiet (having only two fans) and pretty quick to boot (and you can never have too much processor power when dealing with MAME).