If you stick with watching Trek for the time being, go to Enterprise next. With the next movie hitting soon it might be advantageous to refamiliarize yourself with the only one of the six TV series that is now canon in both the Prime and Abrams realities.
If we go by the actual
meaning of the term Canon, TOS (and the TOS movies) has still far greater canonical relevance for STiD than ENT.
For instance, Carol Marcus will appear in STiD, but none of the ENT characters will (neither will they have any relevance to STiD's plot as far as we know).