I quite like the wheel. Played it with the classic also and thats fine.
Biggest impact on the controls is drift/cornering method. If you set it to automatic, the cars steer more sharply. In fairness, this makes the game extremely easy to pick up for newcomers. The missus plays this way.
Me, being a man with an ego, I set it to manual, and promptly got my butt kicked, by the missus. Much to her enjoyment.
If you set it to manual, you have to hop/drift around some of the corners when going at speed as you simply cannot turn sharp enough. Takes a little bit of getting used to, but enables some beautiful drifting. Once I figured it out, I got my revenge..... and was sent to the spare room for gloating

Blue/Red shells are still slightly annoying, but its how the game is. Even if you are last, you know the boxes will have mushrooms/magic stars to help you along. No matter how many times you are hit, you never feel like the race is lost. Part of the reason for its success I suppose.
Btw, I have managed to avoid a couple of red shells, by firing a weapon backwards just before it hits me. Probably more luck than judgement.