I am currently taking a course of (supervised) pulmonary rehabilitation, and the exercise consists of a combination of cardiovascular and muscle-strengthening ones.
Stepping up and down, sit to stand, cycling (on a machine), walking, and weight-lifting (bicep and tricep curls) are the ones we do. The patients are older people with respiratory conditions, so the exercises have been chosen accordingly, and all can be done at home (except the cycling, unless you have an exercise bike). We've been advised to do the squats using a kitchen worktop for support, and to do the sep-ups on the bottom step only, and use the banister as support if we need it.
If you don't know how to do any of those exercises, let me know and I'll explain more.