One use of modal analysis is to understand which modes of a structure are causing a particular dynamic response. Mass participation factors are one way to measure which modes are important and which are not.
You need all the modes in the frequency range that you are interested in, plus a safety margin. Including modes up to 2x or 3x the highest frequency you want to study is often a reasonable choice. If you have many modes with closely spaced frequencies, you need to be careful about this - for example run the model with different numbers of modes and check the results are similar.
The total number of degrees of freedom in the model (or the real-world structure) is irrelevant. The number of modes used is often much smaller. One of the advantages of modal models is that they can give good accuracy with a small model size, once you have found the mode shapes and frequencies (and that only needs to be done once).