A clinical research coordinator is NOT a lab coordinator. A clinical research coordinator (CRC) is often a nurse who works one-on-one with human research subjects. They obtain consent, take vitals, draw blood, teach the patient how to use their diary, input eCRFs and do paperwork under the guidance of a doctor. This position is a good stepping stone to being a CRA.
If you like the lab, forget about being a CRA. Lab work and CRA work do not have anything in common.
I think that a Master's degree often makes entry level candidates look overqualified and it hurts them. A master's comes in handy for a mid-career move- not so much for getting started. Also a Master's on Biology really doesn't have much to with being a CRA- a master's in Biology would be a good idea if you wanted to continue your career in the lab and advance in that position. There are a few Master's programs for clinical research, regulatory affairs, health policy, pharma development, etc. that are a better match for a CRA.