There are a few loaders, I think. But you need your own copy of the game (legally, anyway).

2 answeres:
1.) No GameCube emulator exists for the Wii. So there is no best.
2.) The Wii. But it is not an emulator, it can directly execute GameCube games.

There are a lot of USB loaders and special loaders, that allow loading GC games from USB or SD.

There is a software called Nintendont. It even works on newer Wiis (without official GC support) and on the Wii U. It is the best way to play GameCube games imo because it also has features like emulating a GameCube memory card.

If you have Dios Mios installed, yes, you can use WiiFlow and maybe USBloaderGX. They should work with Nintendont too, but i never got that working.

Dios Mios is pretty outdated and is not necessary anymore. You only need Nintendont for GC games.

NINTENDONT has more support and is much better than DIOS MIOS.
If you have the real game, get Devolution: it supports BBA emulation too if you want that.

you can tell usbloader gx to directly load gamecube games from the GUI..then you have them whith covers and all the fancy stuff that usb loaders have, as nintendont itself has a very simple interface