You might want to take a look at this retro handhelds spreadsheet. You can try filtering out good GameCube support (column S, support level A) and going from there. Good luck!
Emulation
Community to talk about emulation & roms.
RULES:
1.) No bigotry
LINKS:
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Emulation Wiki - Your source for everything emulation :)
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[WIP] Emulation Links Wiki - My personal wiki for emulation links, please help contribute!
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r/Roms Megathread - Megathread of Roms
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RetroArch - RetroArch is the popular front-end to libretro which is a simple API that allows for the creation of games and emulators.
This is amazing, thank you!
Gamecube is old enough that a fairly mediocre phone running Dolphin should be able to do it.
Might not be the absolute cheapest option, but a steam deck is a pretty great solution
And it's also a steam deck.
Maybe look for second hand 64GB models near you if you're on a tight budget, you can expand the storage with an SD card easily
Rg cube. But really a good Bluetooth keypad for your phone like a game sir is going to run better and be cheaper.