The sole Ninth Doctor season is easily
the best way to introduce Doctor Who to a newbie. From the mystery of this "immortal" time-traveller, right down to his regeneration to the Tenth Doctor, this season shows all the beats of what Doctor Who, and what the Doctor is all about. For a new fan, its the perfect place to start.
And I say that as one such, who got into Doctor Who just a month ago, and never looked back. Finished the Tennant years, and scouted throughout the Troughton and Baker years. Its a long ride, but I had to start somewhere, and "Rose" was that place - and I didn't even know what I was missing.
So, yeah, start with "Rose", see the Eccleston-Tennant episodes/RTD's era, and go from there.