You could also use a GameCube Controller, but you will have to buy a USB adapter. This can also be done by installing USB Loader GX on the Wii, which is actually required anyway to legally get your game disks to play on Dolphin, but it is still an advantage over a regular Wii. There are also many community made texture and shader packs which improve the look of the game substantially.
There are hacks that let games run at 60 frames per second. In fact, even games for the GameCube, which had a maximum of 480p and were stuck at a 3:4 aspect ratio, upscale very well to full widescreen HD or even 4K. If you have good hardware, you can crank up the graphics settings on older games.Why do this if you already have a Wii? Let me count the ways: