Best way to move a character (top down)?

I wonder what the best way is to move a character in a top down game view where you can see the small character from behind and the top on a terrain.
I am asking because I have noticed some strange behavior with a terrain when moving a rigidbody. For example: When the terrain has some extruded areas the character is moving through them and dropping through the mesh and falling in nirvana.
I then have tried adding a nav mesh and for the character a nav mesh agent. The mesh then prevents the character from falling BUT I can not jump using the old gravity code anymore.

I wonder if there is some best practice for moving a character and still be able to use physics etc.

How are you doing it?