It all depends on how many people from the U.S. are booked on the cruise and had their Medallions delivered to them. Remember, the Medallions are only shipped to U.S. addresses. There was quite a long line at Medallion pick-up when I boarded a Southampton departing cruise as the majority of the passengers were Brits and had no choice, but to pick up their Medallions at the port.
It also depends on how organized the port agents are. Sometimes there is a long line to pick-up Medallions, sometimes there isn't. The agents, are mostly seniors working part time, and their eyes don't work as well. The writing on the bins and baggies used to organize the Medallions are quite small. If your Medallion is misfiled in the bins, it will take longer to find, as the agent has to shuffle through the nearby bins. If your Medallion is missing from the bins, then you have to wait until Guest Services can make a new Medallion for you and for a crew member from the ship to hand deliver a new Medallion to the pick-up area.
As far as boarding, get a group closest to "1" or "A" so that you can get on the ship first. The sooner you have your Medallion, the sooner you can get a boarding group assigned to you. Having Captain's Circle Status helps, but some passengers lie to get an earlier boarding group. Remember, Princess sometimes issues the wrong colored loyalty status on the Medallion (if this happens, Guest Services can do a swap out) or some people have the image customized, there really isn't a way to verify status just form the Medallion at embarkation. The Elite and Platinum perks are really only loosely enforced at the port. This really only matters if you arrive before boarding; the groups are called quite quickly as soon as boarding commences. This point is really null and void after they are done calling groups. Once, they are done calling boarding groups and getting the initial crowd boarded, approximately 30 to 45 minutes after boarding commences, it's a free for all to get onboard.
Lots of variables can change your experience at embarkation. You are correct in that you should book onboard experiences as soon as you board to better have your desired times available to reserve.