MAME needs very low powered machines to run the good ol' classics.
I say "go for it." I think that you can be successful pretty easily. I am a "keep it simple" guy, and I know nothing about Linux/Ubuntu to help there. I loaded up a stripped down version of Windows XP back when I last loaded up my machine 2 years ago. Windows 7 was considered slower due to bells/whistles of Windows 7 vs XP, and XP working better or older hardware.
Going with Linux/Ubuntu should get more performance from your hardware, but might be trickier to install.
So long story short, you should be playing Donkey Kong in no time once you get the O/S installed.
After you get that working with a TV, then it is just some basic carpentry to build a box to put it in, or heck, just mock it up in a cardboard box and call it good.
