Watch them all. Take a year out of your life and watch them all. Fall in love with every Doctor. Cringe at the early racism and the terrible writing that often happens, love this Doctor and hate that one, fail to see why people like/dislike an episode/serial, and form your own opinions about this and that. The full picture is there and there is no shortcut to the truth.
Or don't.
If you have never watched Doctor Who before, you're going to be lost, but that's part of the experience. There is some serious beauty in this show and you don't have to have the full story to feel it. And that's fine.
But don't take half measures and pretend you've got a full cup.