Like you said, it's a good starting point. I'll nitpick on a couple of issues.
- Many people can't do a proper pushup, let alone a pushup with rotation. Many a shoulder have been injured attempting them by those who shouldn't have.
- Beginners usually have an easier time getting the form right with split squats than lunges. Here is a split squat: www.exrx.net/WeightExercises/Quadriceps/DB
- the workout has no "pulling" exercises (= "upper back") to balance the 3 "pushing" exercises (pushups, chair dips). Usually pushing & pulling sets should be about equal in number. It's hard to do pulling exercises without equipment, but this bodyweight row can work until dumbbells or resistance tubing become available - www.youtube.com/watch?v=9E_1onVeY7k