I took a no longer used 12/2 wire from our backyard and extended it to my new shed so I can wire lights and outlets. The wire is on a 20amp breaker in the main panel, which has 100amp service. My original thought was to install a small two breaker panel (70amp is the smallest I could find), and run lights off one breaker and outlets on the other. After researching online and watching some videos, I am questioning whether this is even possible. It would be nice to have them separate, but am I better off (or have to) running everything on one circuit?
Since the feed from your main panel is on a 20 amp breaker and 20 amps is allowable for lighting and 120V outlet circuits, there's no reason to add a subpanel. The 20A breakers you'd put in the subpanel would be redundant. If you want a master switch in the shed, I'd suggest using a non-fused SPA/air-conditioning disconnect box. These are typically designed for two-leg 240V but you can just use one side.
All of the above assumes that you are in the USA and are keeping the circuit 120V and not 240V.
However, if you want to wire the shed with 14 AWG wire, then you will indeed need to protect this wiring with a 15A breaker, which would "waste" 25% of the 20A circuit capacity. In this case, installing a subpanel with two 15A breakers would be necessary. I would go with 12 AWG wiring…much easier and probably less expensive.
You do not need to install any sub panel, just install your run 12x2 awg which ends inside the shed in an electrical box, obeying NEC article 300 wiring methods. From there you can wire to other boxes for desired outlets and lamp switches. Remember to check your secondary 20amp breaker on main panel, if it's a regular thermomagnetic one, you must change it with a GFCI circuit breaker.
Saludos, Alfredo Padrón