This is just a tip, but depending on the race, you'll want to approach them a certain way.
Car: Any car, though I went with Lola since she counts as both a car and a flying vehichle.
Motorcycle: Any motorcycle other than Ghost Rider's because it's big, bulky, and hard to maneuver in narrow streets.
Van: Captain America's 4x4 was the only one I found that worked.
Flying: Create a flying character in Avengers Mansion with super speed.
Web Slinging:Create a web slinging character in Avengers Mansion with super speed. However, they may be harder to control. I struggled with my web slinger randomly going too high and over the ring.
Swimming:Just use your created flying character. One of the swimming races involves flying anyway.
Boat:Any boat will do.
Acrobat: You can't create an acrobat character, so any acrobat will do. You can even go with a flying character with acrobat ability. However, I struggled trying to get through the rings with flying characters because I kept trying to treat them like acrobats rather than flying characters. If you want a flying character, Crystal is good since she doesn't have Hyper Jump, so you don't risk her not jumping when you need her to jump.