I've camped at Gulf State Park many times over the years. It's a pretty nice campground, but it is a large campground. Some of the loops (especially along the lake) can have quite a bit of traffic through them. Not really a concern unless you've got little ones riding bikes.
I'd say most of the traffic is due to people leaving the campground going to the beach, out to eat, the waterpark, etc.
You'll want to drive to the Gulf. I'd guess you could be a mile or more from the Gulf. In July, you will not want to walk due to the heat.......There is no place to swim in the campground.
which brings up the worst part of the campground: the bathrooms. Unless they've improved the ventilation, the bathrooms are a sauna.
Air conditioned bathrooms and a swimming pool would really make this a first class campground.
If you've never been, be sure to visit the National Museum of Naval Aviation at Pensacola Naval Air Station. Incredible museum, and it's FREE. It's also air conditioned, which is something you'll want to experience after being at the beach in July.
http://www.naval-air.org/