Might sound crazy but if you can get a cheap PS3 and mod it to run Retroarch, that might actually be your best option (or one of your best). I'm sure it would be able to run anything from Atari era to Dreamcast more or less well. You have native PS3 games support (duh), native PS2 (depends on model) and native PS1 (depends on model) support too.
This guide seems to show how you can go about modding a PS3 for Retroarch support.
And a guide for MAME core in Retroarch on PS3.
Usually "PC" would be the go-to answer but PS3 emulation on PC still isn't great, and for decent performance you'd need a pretty beefy setup. OTOH, I don't know if systems like the Saturn would run super-well under Retroarch emulation on PS3.
That
said...
There's this emulator that can do Sega Saturn emulation on PS3 at 60 FPS at HD resolutions. My first time coming across it..runs Panzer Dragoon Saga quite well here TBH (just as good as I've tried it on PC emulators).
Now systems like Wii U and 3DS might not be possible on PS3 RetroArch, but the idea of a modded PS3 for emulation while getting native PS1/2/3 support has always intrigued me, personally.