Just to add my two cents into this... David T. is the greatest Doc from the new series, although Matt Smith has started to seriously carve out a niche for himself. As for eps to watch to get into the show. I agree with the person who said to watch the 1st one of this new series of Doctors. It's a good "never seen this before" ep. Other than that some of the best that have been done are.....
Blink - Season 3 Ep 10
The Impossible Planet and The Satan Pit (two parter) - Season 2 Eps 8 & 9
Stolen Earth and Journey's End (two parter) - Season 4 eps 12 & 13
The Eleventh Hour - Season 5 Ep 1
Those will give you a great feel for the show and imho are some of the best from all 5 seasons.
Also to give you a good line from one of the eps that definitely gives a feel from the show ....
Amy : and here I thought you were just a mad man with a box.
Doctor: Amy listen very carefully because your life may depend on this one day. I am most definitely a mad man with a box!