There are a lot of "experts" out there who are willing to tell you how to get in shape. Most of them want you to pay them first but I can't blame them for trying to make a living. The trouble with it is that if you have never seriously exercised before or haven't in a long time, the different modalities and opinions can be a little bewildering.
I like body weight exercises and I do them mostly in non stop circuits or circuits with very little rest in between. I do other things also but this is my favorite way to exercise. But it's not the only way. And what you do needs to depend a lot on your goals.
If you want to go to the Olympics as a weight lifter, then you need to practice Olympic lifts. If you want to complete a marathon, you need to run. If you want to lose weight and get in better shape, you need to eat right and do something--anything--just move.
The options are almost limitless in what you can do and how you do it. You can lift heavy weights and low reps or light weights and high reps. You can do it fast or slow. You can use kettlebells or clubs. You can sweat to the oldies. You can jog, sprint, walk, hop, jump rope or a host of other things. Or you can do body weight exercises.
The advantage that body weight exercises have over some others is that you need no equipment. You can drop down and do some pushups anywhere. For pullups you can use a tree branch or playground equipment down at the local park. It doesn't cost anything and you can get strong and fit using by using your own body.
Regardless of what method or methods you choose, you need to choose something you like and stick with. The best exercise program in the world (and almost everyone claims theirs is the best) won't do you any good if you don't actually do the exercises.
No, thinking about it just won't cut it. You have to do something. So what are you waiting for? Get out and move already.