Starting Character: Mario
That's not a bad idea, but Yoshi is pretty much useless after you unlock Mario, so he'd get pretty cramped laying in his room all day. Got give the dino a little time air time, right?
Different Courses/Level Changes
That sounds like a good idea. However there were some minor changes to the levels. For example, I'm pretty sure they added some stone platforms behind Whomp's fortress, where you collected the silver stars (I think, it's a long time since I last play that game)
Characters have same moveset
But then what's the reason for having different characters if they all play the exact same? I think the characters should have had more balanced movesets. For example, Luigi can jump really high, but he's slower then Mario. Wario was proably the worst character. There were some areas he couldn't access, but he sure was a powerhouse. However, what's the point of this when all the enemies die in one hit with either character? They should have given the enemies more health so they could not be killed in one hit with any character except Wario. That would have given players a reason to use Wario.
Caps available to all characters
That would have been nice. I think what they should have done, however, is that each character can use the regular three caps from Mario 64 (Wing, metal and invisible) but also have a cap of their own (Balloon for Mario, fire for Yoshi, and something else for Luigi and Wario)
Can choose to do whatever star with whatever character
Again, what's the point of having different characters if they all do the same thing and have the same objectives?
Also, a 4 player co-op mode with all four characters running around the castle would be pretty spiffy, rather then that stupid battle mode we got in the final version.