The transportation and parking link is a good one, but from my personal experience during undergrad, it's easy. The surface lots you're eligible for should be the C lots (I don't think professional students are treated differently for parking permits). I've ordered very early and very late, and never had a problem getting one. The only difference is that if you order early in August, they mail it to you. Otherwise you stand in a LONG line at Bevis Hall to pick it up.
You can also get a CG2 pass, which is what I've been using most recently, as it lets you park in the garages literally across the street from Meiling Hall where you interviewed on 9th Ave. Those are more expensive and you have to enter into a lottery because demand is greater than supply. I've done the lottery twice (I ordered as EARLY as possible!) and got a CG pass both times.
Good luck.
ETA: Both the garages and the "pit" (surface lot on Cannon Drive, which runs all along the med center from north to south) are within a very short, easy walking distance of the med center.
