Look for a second hand Wii U. Plays GC wii and Wii U games with hdmi!
If you want the clearest 480p, the original Wii will do. With component cables and a compatible TV, it should be just as clear as DreamCast VGA.
For many games there are even community high-def texture packs that you can add to make them look even better.
[Edit: Sorry, was talking about Dolphin here, not Wii U!]
Wii U's max HDMI output is 1080p. Also I have not seen any information that it does upscaling at all, so if you have a source for that, I'd like to know it.
There are a handful of GameCube titles that were 16:9 native widescreen on the original console. The one that comes to mind for me is Serious Sam: The Next Encounter