I don't see any reason to get police/medical checks done BEFORE applying or during the first month. Most applications are taking the full 12 months to process, and I haven't seen any processed in less than 9 months lately. I'd say it's best to wait 4 months, lest your application takes 15 months to process as is being estimated.
As you will probably be updating evidence over the course of the 12 month processing period, the whole "its better to get it over and done with" argument is nullified IMO. Usually, you can only schedule a medical exam no more than one week before your appointment. So, it's not like you'll be waiting a long time. Foreign federal police checks take the longest to process.