In which case you can't really go wrong with an Amiga, unless you're looking for something even older. I'm a little biased in that regard as i'm firmly in the CPC camp, however modern Java emulation is now spot-on and you can play all the games on a modern PC. It's worth keeping in mind that the Sinclair Spectrum is in the midst of a revival thanks to its recent Kickstarter campaign, which leaves the C64, Acorn/BBC Micro, and um... Were there any others??
You have to remember that the base versions of each system (Not incl. Amiga or Atari ST) used cassette tape games which could take anything between 10 and 40mins to load, so if you are going to go that way try to get one that includes a disk drive.
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Classic CPC 464/6128 games:
Turbo Esprit, Rainbow Islands, Exolon, Supercars, Oh Mummy, Chuckie Egg, Laserwarp, Cauldron 2, Afterburner, Get Dexter, Chase HQ, Codename Mat, Tau Ceti, Tomahawk, Total Eclipse, Gauntlet, Lotus Esprit Turbo Challenge, Rick Dangerous 2....
There are actually tons of great games on the system now that i think about it, but those load times;