If you are hosting your own site you can look at installing and running a profiler that analyses speed and request processing. Is this for prod? I would need more info on what your app does and what you would like to measure to be able to give you more pointed advice; with JS it is difficult to accurately measure things unless you have the right setup... You might consider applying a method e.g. the scientific method... There are some amazing materials online. Draw from the experiences of others who have been through what you are doing. I have seen some materials on e.g. Flame graphs for traces in streaming environments... Look it up :)
Faraz Syed
Application development consultant
User analytics: start with Google Analytics and also check out Kissmetrics
User interaction analytics: check out keen.io
App performance: check out Keymetrics.io