My general experience has been that for every five driver levels you advance, you advance one position in the starting grid. So the standard progression appears to be:

Driver Level        Grid Position
1                   8
5                   7
10                  6
15                  5
20                  4
25                  3
30                  2
35                  1

However, there are exceptions, notably on more advanced races. There, your car also becomes a factor. It is my current belief that these are your highest possible starting positions; other conditions may lower them. (I've had one race when I should have been position 2 where I started in 3, and another where I was pole and started at position 3.) I need to do more fact checking and verification on how the progression actually works.