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.
"I tell you what you all need, you need to take a thirteenth step, down off your high horse." - Hank Hill, King of the Hill