There is no car park at the lighthouse, because the lighthouse is in the middle of a highway. Park on the beach side of US 90 along the frontage, walk to the signalised crossing at Porter Avenue, and use it. People do improvise a dash across four lanes of sixty-mile-an-hour traffic and it is a genuinely stupid idea, particularly with children.
The city's visitor centre sits on the north side of the highway opposite the tower, which is where the climb is organised from when it is running and where you will find shade, restrooms and somebody who can answer a question. That building is a good first stop in Biloxi generally.
For photographs, the light sits almost due north of the beach, so the sun is behind you if you shoot from the sand in the late afternoon and behind the tower if you shoot from the visitor centre side. The classic frame — white tower, black-tarred base, water behind — is taken from the beach looking back across the road, and it works best in the hour before sunset when the traffic thins and the iron goes warm.
Budget fifteen minutes if you are looking, an hour if you are climbing. It is a stop, not a morning, and it pairs naturally with the Small Craft Harbor a little further east along the same road.