The ODroid C2 has double the CPU of the Pi 3 for $5 more. That's the sweet spot right now, though we haven't been able to get some good benchmarks yet to see how the performance is.
Anything older than a Pi 3 is right out-- you'll be stuck with ancient builds of MAME that are missing a lot of newer games, you won't be able to get official MAME team support on builds that old, and the games will have bugs that will have been fixed years ago on newer builds. In short, you'll have a completely miserable time.
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Try checking the MAME manual at http://docs.mamedev.org
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