Am I required to obtain a student license before a sport, recreational, or private one?
A student pilot certificate is just a medical certificate printed on yellow paper instead of white paper and with endorsement templates for soloing printed on the back.  Other than that presentation difference it is no different than the medical exam a certificated pilot takes for whatever class medical you apply for.  The fee for this varies by examiner and may set you back $75 or so, but that (and being able to pass a medical) is the only barrier to entry.  There is no flight training or knowledge requirement to get this certificate.

Once you have a student pilot certificate / medical you have one of the requirements to solo and can train directly for any of the sport, recreational or private pilot certificates.  You'll want to focus on sport or private training, as pretty much no one pursues recreational certificates.