I would ask for the letters just short of a month into spring semester of 2016 and have all your letter writers submit the letters to Interfolio a month before those spring classes end, that way your letters are done before the big end-of-semester push. I followed a similar timeline for the current application cycle and it worked perfectly. This way the letters are more current, and a month into spring classes is not long enough that professors from fall (if you are asking any of those for a letter) will forget you.
Edit: Also get extra letters if you can. I got 1 from a professor in my science department, 1 from a science professor not in my department, 1 from a professor not in a non-science department, 1 from a work supervisor, and 1 from a volunteer supervisor, and that was sufficient for every school I looked into except for Thomas Jefferson I think which requires a physics professor(?); I can't quite recall.