You just mean for races on normal/b rank? Or world tour events on normal?
For races at least; try giving the time trial a go - follow the ghosts with the best times, it helps you to learn the best routes to take for the fastest lap times, and helps your general track knowledge.
It's best to go for a character with 4+ speed and 3 or 4+ boost on tracks that aren't too complex (such as Ocean View or Carrier Zone), and/or that you feel confident that you won't crash much, as you'll be able to obtain a resonable speed. Whereas with tracks like Graveyard Gig and Burning Depths are more complex and have some tight turns, you'll want a character like Amy; someone with good handling to manage those twists and turns, and with good acceleration too, so that every time you crash, you're able to quickly re-gain top speed.
A nice little trick to help come in the top 3 of a race, is that if you aqquire an all-star pick up, to save it for the last quarter/half of lap 3, so that you can boost your way up to the top spot (if you're not already) right before the finish line.