MAME is almost entirely dependent on CPU power. Any idea what kind of 1GHz cpu you have? Keep in mind that modern onboard video almost always uses system memory for frame and texture buffers. This will eat away at your 256M. Exactly how much depends on the video chipset, and your BIOS settings.
XP will be gasping for air on a sytem with 1GHz and only 256M of memory.
I wouldn't even think about running XP with less than 2GHz and 512M of memory. Though some people will call me crazy. I can hear them sharpening their pointy sticks already.
However, if you can bump your memory up to 512M, drop back to Windows 98SE, and resign yourself to only running older versions of MAME (someone here will have to offer specific version numbers), I think you'll make out fine.
Depending on the exact chips used for your onboard video and sound, you might make out better picking up a used soundblaster and Geforce2 off of eBay. Sometimes, the onboard stuff *REALLY* sucks and eats up a bunch of CPU cycles while it's sucking. Without knowing the exact details of your hardware, it's hard to really know.
Your hard drive should be fine. A full set of MAME 0.92 ROMs, CHDs and samples is only about 40GB so you should have plenty of space even with newer versions. I can't imagine it's gone up that much with the newest version of MAME.
If you decide to go with 98SE, make sure you install the Unofficial Windows 98SE Service Pack...
http://exuberant.ms11.net/98sesp.html