I tried out that Beginner's calisthenics class we posted this past week. Even though the class was coached by three smiling girls who never broke a sweat, I found keeping up with their pace challenging and I did break a sweat.
I would recommend it as an excellent first-thing-in-the-morning daily light warm-up/workout for beginners. Since no HIIT or weights (only hand-weights) are involved, no recovery is needed so you can do either weights or HIIT cardio on the same day with no problem.
Remember that calisthenics like these are for athleticism, light cardio, and general fitness maintenance. There is no strength gain or cardio gain involved, but that is not what it is for. I did feel great after doing it. If you are new to the fitness cult, I'd recommend this as a daily morning routine before advancing your program too much further.
Yes, I would advise first thing in the morning, right after slugging down a quick cup of coffee and before opening your computer. Unlike an hour of heavy calisthenics, this will leave you pumped up for the day instead of ready for a nap.