I also agree with Karin, it really depends on the individual client.
Self-esteem and body image are a few issues that will help you determine where to start with this population. You will need to be sensitive to their needs and understand that many of the standard fitness assessments will not be practical to use with this population. It may or may not be practical to assess body composition on some obese clients. Calipers and circumference measures may be invasive or uncomfortable for this population (certainly it would help to have this baseline but again, depends on the individual).
Helping the client understand the role of any assessment you choose–and how it may relate to activities of daily life. For examples of fitness tests, a squat test may work for this population and you can help them understand the functional aspects of performing this exercise. Endurance tests may not be needed since it may be clear that it will result in an uncomfortable/poor experience for the client. If they are winded walking a block or two, this may be your baseline. Getting up and down from the floor can be difficult, so I would avoid fitness assessments on the floor. Postural and range of motion assessments may work just fine.
Build a rapport with the client first and assess their level of comfort. Exercises or assessments that are related to their activities of daily life will help them understand how exercises can improve their daily activities.