As a total beginner, you can start anywhere. Anything is better than nothing. But pretty quickly you'll hit some limits. You'll quickly get strong enough that the kickbacks, planks, and squats aren't doing much of anything. The mountain climbers will be more cardio than strength work. Push-ups are pretty solid, especially if you can start elevating your feet once you get past 20+ reps. After that you'll probably want to get a dip bar (something like this) or do dips on rings. Once the squats get easy, you can start doing variations that work one leg more than the other, like modified pistol or shrimp squats. For example, sit down on a chair and stand back up, but only using one leg. Step-ups and lunges can also be in the progression. You'll need a pulling exercise. For now, get under a table and do inverted rows, like this. If you end up getting those gymnastic rings I mentioned for dips, you can do inverted rows at various heights as you get stronger. A pull-up bar will be another good addition. Dips, pull-ups, and single leg squats will cover your bases decently well through the intermediate level. After that you'll either need to explore advanced calisthenics/gymnastics moves, or get access to heavy weights.
