Severian's advice seems sound. Tennant is a great Dr. and a perfectly good one to start with, although the stories are a bit darker and more complex than previous incarnations so in that respect they're not necessarily typical. If you do want to watch some of the earlier stories that are considered classics, I'd recommend:
Dalek Invasion of Earth (William Hartnell as the Dr and a classic Dalek story but maybe a bit old fashioned for today's tastes)
Tomb of the Cybermen (Patrick Troutman as the Dr and includes the cybermen - who are even better than the Daleks, imho)
Terror of the Autond (Jon Pertwee as the Dr. This one introduces the Dr's main antagonist The Master)
Genesis of the Daleks (Tom Baker era. Introduces
Davros, creator of the Daleks and probably the greatest most iconic villain in the series ever)
Pyramids of Mars (Tom Baker again. Includes Sutek'h, who scared the living shit out of me as a kid)
Those could be considered kind of like the foundation episodes for all that was to come later on. You'd understand everything perfectly well without them but if you're someone who likes to know the context those are a must. I think most are on DVD but if not, you shouldn't have a problem DLing them.