In my group bootcamp classes, this is somewhat driven by how many people are participating, and what their goals are. In general, easy assessments to benchmark beginning and ending cardiovascular, strength, & flexibility gains are what I do. These can be easy tests, such as a timed run/walk test (on a premapped distance), timed wall squats to failure to assess lower body strength, push-up test to measure upper body strength, sit-up test to measure abdominal strength/endurance, sit and reach test for flexibility, etc…work well in a group setting. Using this method, I’d measure a beginning result, and follow with an end of session result…normally about 6-8 weeks after the first testing. I’ve often accompanied this with a benchmark weight (pre-post session), and basic body composition measurements.
(In a smaller, small group training situation, it’s more possible to take more complete and detailed measurements.)
The bottom line is that in a large group setting, measurements should be pertinent to the exercises you’ll be doing in class, should be easy to administer with minimal equipment, and should be repeated at the end of the session (6-8 weeks after initial measurement) to measure progress.