Most people don’t notice the subtle drops in weight/inches. But they do notice if breathing becomes easier (during an exercise or just in daily activity) and whether or not their clothes fit better. Progress pictures are great. Many of my clients like to see the numbers change, so if they are open to it we do measurements and body fat %. I don’t like to go by the scale, it’s a fickle instrument, and I don’t have access to the more technical tools.
I do like to have a baseline workout that I will put clients through on their first session, mark down how many reps of each exercise are done in a certain time period and what their physical response is, and then revisit that workout two or three months down the road to help them visualize and understand how far they’ve come.