50cc and 100cc should be easy enough that you can use any character on any kart or bike and still win.
Baby Daisy, Daisy, and Funky Kong all give a hidden speed bonus to whatever kart or bike you use. Bikes are the best ones to use because you can do wheelies whenever you want which helps give you a boost. Bikes with high drift are best because you can make sharper turns very easily. There are karts with high drift that you can also use. High drift basically makes you drift inwards. Low drift makes you drift outwards (like in Double Dash).
I had difficulty with the Banana cup on 150cc and Mirror. Sherbet Land and Shy Guy Beach are my 2 worst levels. If you have trouble on Shy Guy Beach, the best way to beat it is using Toadette with the Magikruiser. Toadette gives a hidden bonus to offroading and the Magikruiser has the highest offroading of any bike (have to use a bike when offroading because you need the wheelie to boost). You can cut the corners the whole way and barely lose any speed. Here's a video on how to do it exactly.
Some people say it's cheap. But so are the crabs and blue shells
