It is pretty cheap to try an OUYA for $60-$80.
If it were me I'd just order the Anthracite model from target...Updated wireless and controller...was on sale for $79.
I have OUYA and a modded gamestick.
Both run super mario 64 & smash brothers 64 without complaints from my kids.
Ouya can run the HD textures though for both games while gamestick can't.
plus ouya has nostalgia front end for emulators.
psp emulator i've only played with a little and it seems to run equally on both gamestick & ouya but i havn't used it a lot due to configuration is a pain.
have not tried reicast either.
If you want to run gamecube then PC is the only option.
same with ps2.
I have an athlon x2 sitting around I plan to try ps2 emulator on.
not sure it will have enough oomph to run games though even at native res.