How far do you want to travel? It says you are from Ontario, are you coming in to Michigan at Detroit/Port Huron or at the Soo?
Three parks come to mind with what you describe. They are Sleepy Hollow, Ludington and Wilderness. Sleepy Hollow might be considered outdated to some of the state parks like Holland and Grand Haven that have been updated. But there are several private camp sites and they have hiking trails around the park.
Ludington offers everything you mention. If you are considering camping there, mark your calendar 6 months ahead of your trip to make your reservation as that park fills up fast.
Wilderness State park west of Mackinaw is also excellent.