echo on:
What monitor will you use?
Arcade CRT, pc CRT, LCD
What games do you play?
This used to be a common questioned with a reply along the lines if it was pre Street fighter you could put in any machine from the garage.
Will you connect this to the internet?
If so, consider this step of the project as buying a PC that will connect to the internet. As such, buy a PC that runs the latest version of Windows. It doesn't have to be an F1 racer of a machine. Just a CJ that can go anywhere.Consider the following:
Do you have old PCs with OS keys you can use? Do you have a box of PCs maxed out with ram? Where are you starting at is the most important question we can reply with. Run mame now on your current machine, then upgrade what you need until you are satisfied. Upgrade until it hurts.
Do you maintain an index of roms per version of mame that plays on "any old machine"
Ultimately, as with upgrading any PC, this will come down to a cost benefit situation. Not to mention you will spend in man hours of troubleshooting getting different romsets to work on outdated pc platforms.
I've waxed on and on for years OP; without a mame machine that I played for more than a few months - so take this with a grain of salt.
Since dual core is all you need, if you want to keep the cost down and are going with new parts, I would say a Pentium G3258 with a $50 H81 motherboard and 8gb or RAM would be sufficient. The G3528 runs at 3.2ghz and is a dual core processor. You can get one for $65 regular price, or around $50 on sale. Add a $30 power supply and $30 8gb ddr 3 ram and you are at $175 or less before adding an OS. Intel integrated graphics will probably be sufficient, but you could always add a video card later.
If you don't mind used you can find off lease/refurbished 2nd gen i5 desktops for under $150 on ebay, and if you troll CL you may get lucky and find a deal. I scored a 2nd gen i5 laptop with 8gb of ram and a broken screen for $75 a few months ago. I am going to use it in my bar top build. 
I 100% agree with processor - fantastic ratio power/price but should be overclocked to at least 4.0 GHz (with ease on H81 boards with overclocking option). Also 8 Gb RAM is too much, for XP 2 Gb and for 7x64 4 Gb is more than enough.
Please note that some old intel integrated cards does not work anymore with mame. Better choice is to grab some cheap ATI HD4xxx serie if You are going to use groovymame or cheap Nvidia card.
Isn't there an underlying matter of how modern hardware works together? AMD+AMD Radeon= works with better with less hassle than AMD+Nvidia? Maybe we are past that point. *shrug*
Good luck, upgrade your current desktop until it plays your favorite games well. Then you are done.