I agree with Wendy. Using a “mix” is what I will usually shoot for when working with a new client. Body weight exercises can be made challenging and fun, but using external resistance can be used for a wide-variety of “other challenges” such as isolation to help strengthen a particular weakness. Also, as with many beginners, machine weights can be used to enhance their strength in a safe way that could later translate into their ability to better handle their body weight.
Body weight training is not the beginning stage. It all depends on the forces applied to the movement. For example doing a push up on the ground is much more difficult that doing press on a bench (despite what many think).
Therefore, each position relative to gravity should be considered before determining the sequence of exercise.
Fuel the Movement,
It all depends on the assessment and the goals of the client. My typical client is usually deconditioned and/or has a list of conditions that I need to consider. My first goal is to get them to the point where they can control their own bodies, but that does not mean that we do body weight training (and I assume that most people do not consider it to be body weight training to teach somebody to get up from a chair unassisted).