Just to round out the good info already here - I would absolutely recommend coming in to OCS able to get at least an excellent on the PRT, if not max it out from the get-go for the sole reason that it will make your life easier while you're there. First off, the people that suck at PT get hounded by the DIs and CPOs, and once they form a low opinion of you based on your poor PT performance, it is hard to get rid of it when it comes to other stuff. Crushing morning PT and scoring towards the top of your class on PRTs is the easiest way to get them off your back - or at the very least not bring additional pain upon yourself. A lot of people show up for OCS in pretty bad shape - I saw an average of 6-7 people per class roll during the first week (IST and Welcome Aboard) while I was there, which is just being physically unprepared. If you show up able to do anything less than 'Good,' in any category, there is a strong chance you'll roll in the first week.
My advice is to be working out almost every day, mixing it up with weights, runs (fast and short, no more than 3 miles), and zillions of pushups and situps. Chest days should pretty much just be sets of pushups, with different variants thrown in. It's not a requirement, but I can guarantee that if you show up in great shape, when the DIs are looking for someone to scream at, they'll pass right by you and ruin someone else's day instead (assuming you're not all jacked up in another way, in which case get on your face).