Overall
There is currently two devices that I can recommend overall for essentially every system on this list and it’s:
AYN Odin 2 Portal
AYN Thor
For more devices and more systems, see all of the below to get some more ideas.
Nintendo 64
For Nintendo 64, you want a device with power that can handle the emulation and a 4:3 aspect ratio, which makes the Anbernic RG476H the winner.
Nintendo 3DS
The AYN Thor is the defacto best option for Nintendo 3DS games due to its dual OLED screens and powerful processor.
Nintendo DS
The AYN Thor is the defacto best option for Nintendo DS games due to its dual OLED screens and powerful processor.
Nintendo Game Boy/Game Boy Color
Nintendo Game Boy and Game Boy Color games are super easy to run, on almost anything. If you want the absolute best experience though, I’d recommend the Retroid Pocket Classic.
Nintendo Game Boy Advance
Nintendo Game Boy Advance is pretty easy to run, and can work on almost anything, but if you want a nostalgic experience – the Anbernic RG34XX is pretty good.
Nintendo GameCube/Wii
There’s many options for Nintendo GameCube and Wii, but my personal favorite is the AYN Odin 2 Portal.
Nintendo Switch
Nintendo Switch emulation on handhelds like this can be hit and miss, but the AYN Odin 2 Portal would be the best choice.
Nintendo Wii U
Nintendo Wii U emulation is still in its infancy for these handhelds, but the best choice currently would be the AYN Thor.
Sega Dreamcast
For Sega Dreamcast, you want a device with power that can handle the emulation and a 4:3 aspect ratio, which makes the Anbernic RG476H the winner.
Sony PlayStation 1
Sony PlayStation 1 games are very easy to run, and so it all comes down to screen, ergonomics and the rest. I think the Anbernic RG476H is one of the better devices for PS1 games.
Sony PlayStation 2
Sony PlayStation 2 games are hard to run, well, a lot of them are and so it’ll be a tough experience no matter what handheld, but the best I’ve found is the AYN Odin 2 Portal.
Sony PlayStation Portable
Sony PlayStation Portable games are fairly easy to run and so you have a lot of options to choose from for 16:9 devices. However, the best would still be the AYN Odin 2 Portal.