I agree that you would want to stretch the muscles used as much as possible. If a client has a particular over tight muscle group or groups that is causing issues, you could stretch that group or groups first and then do other muscle groups as time allows.
It is pushing people with limited time to ask them to try to do more later and likely to be met with limited success as well. But I would at least approach the subject of taking a brisk walk berfore/after dinner. And then strecthcing properly after the walk (bike ride, swim, etc.) to get the muscles prepared for a stretch intended to promote ROM/Flexibility. This will also give them a second bout of exercise to help increase their fitness and other benefits depending on their goals that may encourage compliance.
And as stretching is one of the most frequently omitted pieces of the exercise puzzle, it is important to impress upon clients how counterproductive it is not to stretch. While there is a great deal of controversy as to stretchings contribution to fitness, a wide margin separates the science that has shown benefits and importance compared to the very small amount that raises questions as to effectiveness. I could go on (and on), but will end here. Anyone reading this that would like to discuss it further, please feel free to contact me through my profile.
In what activity are the participants engaging? That can make a difference, depending on what muscles they’re using the most.
If you’re short on time, rather than skipping any stretches, my first suggestion would be to combine two stretches at once. For example, you can stretch chest / back / shoulders while standing in a calf stretch or a lunge. Then, you don’t have to reduce the amount of time in any stretch or the number of stretches, you’re just doing it more efficiently by doubling up.
But if push came to shove and a client told me they would only do three stretches, period, in the upper body I’d do something to open up the chest and retract the chin. In the lower body, I’d do a calf stretch (on each side), and a lunge to get at both the quads and the hip flexors. With most of my clients spending hours a day at the computer, the chest is tight and closed, and the hip flexors are short and tight so this is sneaking a bit of corrective stretch into their lives. And our feet take a beating all day in and out of class, hence the calf stretches.