The GameCube is my favorite console of all time. The best for local multiplayer and it has (in my opinion) the best exclusives of it's time.
Dolphin can run every GameCube game, it doesn't mean that every game is emulated perfectly. Some might crash midway through the game and some might have sound bugs/graphical bugs that make playing them an annoyance. Here is a great resource into the compatibility of all the games:
https://dolphin-emu.org/compat/ Dolphin can also run Wii games (not all of them though) but some games are a pain to play if you don't have a USB sensor bar and a real Wiimote/Nunchuk.
The best thing about Dolphin to me, is the ability to play almost any multiplayer GC title online. Unfortunately, it's a bit finicky and if one player has a bad connection, the save files on all sides are not the same, or someone does not have a fast enough computer, then the game might desync. Some games don't run on netplay (Some EA Games titles give black screens). Once you overcome all of the problems, you will get the satisfaction of being able to play Mario Kart Double Dash and Mario Party online. Wii titles are only playable if they do not require a Wiimote to play. If it does, you're shit out of luck for the moment since Netplay does not support Wiimotes.
Dolphin can also upres most games into being 1080p and can even increase the frame rate of some titles from being god awful to enjoyable (Little King's Story comes to mind)
The good thing is that Nintendo is still producing Wiimotes, Nunchuks and even GameCube controllers because of the Wii U.
There are 3 different GC controller adapters that I would recommend:
- The Official Nintendo Wii U Adapter (requires third-party drivers but has superior build quality) (might be out of print, they seem to come back in stock every now and again)
- Hyperkin's Adapter (Great build quality, no drivers needed)
- Mayflash's Adapter (Officially supported by Dolphin)
Buying an official GameCube controller and an adapter costs more than just buying a USB GameCube pad but it will definitely last longer than a third party one.
Here's a tutorial in getting an official Nintendo adapter running on PC