Whovians: Where should I start?

ruouttaurmind thought this was worth mentioning said
13

I have never watched an episode of Dr. Who. I did watch Torchwood and enjoyed it.

If I wanted to wet my feet in the Whoniverse, where should I start? If I am not mistaken, there have been many Doctors over many years. Can I pick up with the 2005 revival and not miss any pertinent plots or characters?