We've stayed there many times and now live a few miles from the park because we grew to enjoy the Sarasota area so much.
As mentioned in the first response, June won't be crowded unless there are family/friends groups in adjoining campsites on the weekends. It's a great time to visit the area after the snowbird traffic subsides.
Check the Reserve America description but I'm pretty sure all sites have water and electric, and no sites have sewer. There's a dump station. Rental canoes are available. Wifi at the little nature pavilion by Lake Osprey. Great bike riding on the Legacy Trail.
The north side Sites are along South Creek, but if you have a dog, note that no pets other than service animals are permitted in those sites, #68 through 98. Some of those sites have nice views of the creek not obscured by foliage. This park has five restrooms/shower houses, a pretty short walk from any site.
My favorite pet-approved sites are on the west curve, numbers 64, 65, 66 and 67. They feel more private and spacious to me, and in my memory are quite level.
Lots of grocery and other shopping nearby in both directions. Turn right (north) going out of the park on Tamiami Trail (41) and you'll come to a big Walmart superstore and post office, further along to a shopping center in Palmer Ranch with a Publix grocery store, Target, Walgreen's, etc. and Palmer Ranch Animal Hospital, a good vet. Next shopping center past that has Costco.
RV World is a mile south of the state park if you need any parts or repairs. Big dealership where we bought our current RV.
The beaches are to the west on the Gulf of Mexico. Nokomis Beach isn't far. Siesta Key is also close. For restaurants, Casey Key Fish House is a casual joint we like on the water nearby. Drive along Casey Key's road to see some incredible waterfront homes.
Sarasota has some world-class attractions - the Ringling Museum as noted (circus museum is one element, along with European Art, Asian Art, the Ringling mansion on the bay, etc.) Also visit Marie Selby Botannical Garden, Mote Marine Lab, and more.
Good suggestion re Myakka River State Park. They have air boat rides where you see dozens of gators - you feel like you're in the Everglades. You could get a campsite there or just visit for a day excursion - not very far from Oscar S.
Enjoy. We love it here.