1st thing.... just toss Window ME in the trash. That is were it belongs.
I have 4 HP Pavilions that came with ME.
window XP with sp1 or no Service pack works. service pack 2 seems to kill these old HP's
98SE works great (window ME is a hog)
I used Mame 56 with 512 meg of ram. (well the HP mother boards manual said 512 was the max...

300 is all that would show up

finding the Roms for the older Mame versions can be a bear.
every time Mame upgrades the Roms change also .
So if you get Mame 56 (witch will run almost all the Roms on your 700meg CPU) the newer Roms will not work ... Not even Ms Pacman
Their is programs to back date your Roms.... I for one have yet to get a good set this way. but others seem to have no problems
I very seldom upgrade my Mame
I have 36, 56, 87,88,89, 99 ... never updated the Roms. burned the older set to DVDs and stored them away.
I have had many old PCs given to me. 300 and 400 meg cup's Mame 36 gets these PCs 500 to 900 meg CPU get Mame 56
only my 2.6 gig CPU get Mame 99
I have no reason to upgrade Mame any more.