1. A grout brush works better than most toilet brushes because you can get under the rim more effectively. Put some cleanser (I like Bon Ami) on the wetted bristles and brush under the rim. This loosens the dirt. Brush again as you flush to wash the dirt down the toilet. You can use cleanser in the bowl too. It works as well as a toilet bowl cleaner.
2. Use a pumic stone to get mineral stains, like the one that man times rings the bowl at the water line. These things work great and don't scratch. You can find them in hardware stores or the supermarket.
3. When you flush after cleaning (and in general!), close the lid first. This prevents aerosol spray from dispersing through the room.