There's a couple of lots owned by the amphitheater and there's several offsite pay lots, the offsite lots are going to be a longer walk in but you'll probably get out of the parking lot quicker.
There's two main amphitheater lots (if you google 2002 lakewood avenue you can see what I'm talking about), the one to the west is paved, smaller and includes the VIP parking. This lot is accessed from Pryor Street. I've never Buffetted in this lot and I don't think you can easily get from this lot to the gravel lots located on the other side (the amphitheater and the Screengems studios are inbetween and everything is fenced so if you're meeting friends you might want to make sure which lot you'll be in beforehand.)
The gravel lots are to the east and southeast and surround Lakewood Fairgrounds Lake. This area was once the Lakewood Raceway and the lake is in what had been the infield. These lots are larger, gravel, where most of the motorhomes park, have portajohns (not saying the paved lots don't), and seem to be where most people try and park. Access is from Lakewood Avenue and cost had been $20 per car, more for busses, campers, trailers....
As far as time, the more cars that collect along Lakewood Avenue the better. Advertised opening is usually noon but if all those cars start clogging Lakewood Ave the police cause the gates to open.