Okay so something like a Mini-ITX with Intel i5 or i7 would be good? What about video card? If I'm just planning on using an LCD in the cabinet, is it worth putting in any sort of graphics card? Do people still use Ultimarc's ArcadeVGA?
Do you plan to use MAME's HLSL effects?
(scanlines, glow, etc)
If not and you don't plan on running anything other than MAME, the graphics card is pointless.
If you do drop money on a graphics card, get something new (along with a new OS) that can do Directx 11.
That way you can add Demul and newer PC games later if you choose to.
The last version of MAME I tried was v.170, but here's my $.02 anyway.
For strictly 2D you'd probably be fine with an i3 or i5 in the 2.4 Ghz or faster range.
(can't tell you 100% for sure without using it myself) Modern marketing has stopped mentioning clock speed, but it still rules for emulation.
If it were me, I'd drop the extra money on a 3Ghz processor just to be sure.
There are now drivers in MAME utilizing more than 2 cores, but the ones I've seen mentioned were 3D hardware, so for 2D you are probably fine using an i3.
Maybe Haze can comment on that.
Really though if you're only interested in 2D stuff and aren't worried about HLSL, any abandoned PC found near a dumpster can do it if you use an old enough version of MAME.