The verification process takes 6-8 weeks. July is peek season, so assume it will take 8 weeks. To get secondaries back immediately, I would submit by the second week in July. Schools will not even notice your application until they receive your scores in September. They get 7k+ applications every year. You won't annoy them because they won't take the time to look at it yet.
Its the general rule to get secondaries in ASAP but not to sacrifice quality. Schools actually give you a deadline, but if you are submitting around that deadline, you are LATE. I would get a secondary in AT LATEST 2 weeks after you receive it. Try to aim for a week though.
LizzyM is an adcom member who frequently posts on here. Her method gives you a numerical way to pick schools. It is an equation: (MCAT Score) + 10 x (cGPA) = LizzyM score. What you are going to do is this
1) Calculate is for yourself when you get your scores back. For example, if you make a 30 MCAT then your score is 30 + 10 x (4.0) = 70.
2) Calculate the LizzyM score for the schools you are interested in. Use the MSAR to find their average accepted MCAT and GPA and plug those scores in
3) Here's the subjective part. If your LizzyM score is relatively the same as the LizzyM for the school APPLY. Don't ask me what is "relatively the same." That is up to you and how many schools you want to apply to
4) Add some safety schools. These are schools who have a LizzyM score well below your score
5) Add some reach schools. These are schools that have a LizzyM well above your score and you are really interested in them. Since you are URM you can shoot for the moon here. High ranked schools are known for actively recruiting URMs
6) Apply, interview, and have fun!
