I'm going to assume that you aren't necessarily applying this MD cycle, because you don't sound as if you're in a hurry to get that application. Sorry if I'm wrong and you just don't fit the typical anxious pre-med stereotype (like me a year ago!).
I journalled for awhile to help me prepare for my PS, and several very kind non-trads on this forum read my PS for me. You should absolutely get someone, preferably a current med student, to read for you. This is a good time to find readers, as most students are on summer break now.
Obviously you want a completed PS at the time you submit your (primary) application.
Some schools have essays/short answers as part of their secondary, some do not, so you would need to check on the schools you are applying to (there is a thread in pre-med that addresses this, but it may also be on the school website). I recommend doing a search on "University X secondary" in the forums to find out what it is -just check the date to make sure it's for this year.