What do you breed for?

I am curious as to what others think is important to breed for because I am kind of confused on that part. Is it best to aim for stat points, conformation, or coat color? Or is there one better to aim for first and then go after the other? And also, how do you get the conformation ratings to go up? To get to excellent do you just breed good and good together and randomly get excellent?  TIA

~E

If you throw "conformation" into forum search then you'll be able to find some former discussions describing breeding for conformation.
One of them is here: https://www.equiverse.com/topic.php?id=3201&page=1

I only breed for low NSS and ignore conformation entirely.

I breed for low NSS, high conformation and high stats. Priority in that same order. 
When I created my new herd I used credit items to get the coat color I wanted right away (because you can't get chestnut Friesians from the EC).