Speeding 1 to 5 mph over the limit
MCL 257.320a(1)(q) assesses 1 point for exceeding the lawful maximum by more than 1 but not more than 5 mph. On a limited access freeway on which the maximum speed limit is 55 mph or more, MCL 257.629c(1) applies instead, notwithstanding section 320a, and puts 1 to 5 mph over at 0 points with a $10 minimum fine.
What the points do
A Michigan court that convicts a driver of a moving violation sends an abstract of the conviction to the Secretary of State, and the point value from the schedule in MCL 257.320a attaches to that abstract. Points stay on a record for two years from the date of the conviction. A non-moving violation produces an abstract with no points on it, which is the whole of the difference behind a plea to one. How points reach the record goes through this in full.
The basic driver improvement course
This is the kind of violation MCL 257.320d covers. Whether the course is open to you personally depends on your own record and license: the statute also asks about points already on the record, a commercial license, a previous course, and several other things this page cannot know.
This is general information from a driver-safety school. It is not legal advice. Your court can tell you what it requires, and an attorney you hire can answer questions about your own case.