Here's my advice, and this is how I very succesfully built my mame comp. Go to a hardware forum, not byoac. People will know more about building their own computers, it's where I did a lot of my research. Also, in general they will rate your system (i.e. you list out the components you want to buy) and give you advice. Make SURE that you mention this computer is for a specific purpose. Mame needs processor speed and ram, video card is the third on the list. If you are going only for mame then don't waste your money on a top of the line video card unless you find a really good deal.
I'm assuming you have at least some knowledge of a computer's innards, and if you do then it's not that hard to build one. Especially considering if something goes wrong, you've already got your current computer to look on the net for troubleshooting tips.
www.sharkyforums.comwww.hardforums.comThose are some good places to start.
If you want reviews of hardware check out
www.tomshardware.com www.sharkyextreme.com www.anandtech.comanandtech has GREAT forums for finding deals on hardware. so does
www.fatwallet.comIf you are looking to save as much money as possible then be patient. Decide at least vaguely what you want in your computer, for example what kind of motherboard and processor (amd or intel?), what kind of ram and how much (pc2100, pc2700, rdram, 256megs, 512 megs?), and then look for deals to pop up on those forums and in your local ads. Chances are once you start buying there will be at least one good deal a week for something you want to buy. Over time your comp falls into place!