I think this console is really just one for the collectors. If you're just interested in playing the games, emulation is the way to go (especially as you can get all the games/ROMs that way).
There's the Wii, as has already been mentioned, which can be easily modded. Downside is that you'll need to also pick up official Wii controllers (or GameCube ones) to play, which ain't cheep.
There are plenty of emulators that run on Windows and Android, and most work with modern controllers plugged in (wired XBox 360 and XBox One controllers seem to work the best.
If you want a dedicated machine to plug into the TV and be you main, permanent retro console, then Raspberry Pi is the way to go. For the device, a case, a SD card, a HDMI cable and a couple of controllers you're looking at about £40 and a bit of effort, but I think the result is better.