Re: How to begin?
I would say, pick the ten best episodes of TOS by fan consensus and watch them. Then watch a lot of TNG and DS9. If that doesn't make you a Trek fan nothing will.
Why? Why should someone bypass TOS for TNG/DS9 when they were seemingly drawn in by the big-screen action-adventures of Kirk and Spock. That would be like me telling someone who liked First Contact
and an episode or two of TNG to go watch TOS instead.
"...the most elementary and valuable statement in science, the beginning of wisdom, is I do not know." - Lt. Commander Data, "Where Silence Has Lease"