I generally want to play the games at their best version possible, limited by the fact that if I bought it before and upgrades are purely cosmetic I will not buy the new version. This means that generally I would prefer emulation but not always.
My attitude comes from being a PC gamer, After installing a game, the first thing I do is check PCGamingWiki, Nexus Mods, and ModDB to see what is available to improve the games graphics, sounds, UI, fixes that developers did not do. So, I am always looking to play the best possible version of the game rather than the one that was limited by its time period.
With consoles, I do consider that certain approach of how it was meant to be played is required. These are games that supposed to work on the controller while sitting on the couch. With Wii, they might have been meant for that motion controls interface.
I own a fat fully backwards compatible PS3, Xbox 360, Xbox One X, Wii (backwards compatible to GameCube), WiiU. This allows me to play a lot of older games without emulation and so experience them as such. However, I play my Wii games on WiiU, I play many Xbox 360 and original Xbox titles on Xbox One X, because those console provide some improvements to the old games. There is also one key parameter all these consoles have - HDMI port.
For consoles without HDMI port, I rather emulate on my other PC that has RetroArch installed. And, I got older Logitech controllers to use for that controller interface experience.
I have not tried Dolphin emulator but it can accept GameCube, Wii, and WiiU disks through PC’s DVD drive and able to do wonders there. My only concern would be how those motion controls would work.