I assume the rank you have on your stable is either based off of placings or winings? Is it both or just one or the other? What are the different ranks and how much (winnings, ribbons) so you need to get there?

From the game guide:

Stable Ranks Your Stable will gain rank based on how many blue ribbons you've won. This is listed under Achievements on your Stable Page. The ranks are:

Less Than 10 Blue ribbons - Training
10 Blue ribbons - Schooling Bronze Medal
50 Blue ribbons - Schooling Silver Medal
100 Blue ribbons - Schooling Gold Medal
500 Blue ribbons - Open Bronze Medal
1,000 Blue ribbons - Open Silver Medal
5,000 Blue ribbons - Open Gold Medal
10,000 Blue Ribbons - World Bronze Medal
50,000 Blue Ribbons - World Silver Medal
100,000 Blue Ribbons - World Gold Medal

Thank you!