The Star Trek film and television media I would recommend:
Number 1: Star Trek The Original Series, (Completely optional Animated Series if you loved that and just want more) then Star Trek the original films.
Number 2: TNG, First Contact, DS9.
(Voyager, I do not like it but some do, Enterprise you might as well at that point, if you have got this far)
Number 3: Star Trek 09, Into Darkness, Beyond.
Current stuff: Strange New Worlds, Picard Season 3, avoid 2 and 1, hopefully both shows fulfill their potential.