I quite like Matt too, but never having watched the tennant series I don't have the same reference point others do.
You're robbing yourself if you don't watch the first 4 Series before Matt Smith. Eccleston is pretty brilliant as the doctor as well. You can skip a great deal of the Catherine Tate episodes if you want to, though, as most of those are just a build up to the last of Tennant's run as the Doctor.
I wonder how they are going to resolve RS. They can't really have two time lords, can they?
But she's not REALLY a time lord. She's got human DNA, just with extra bits.
I've downloaded a program called Expat Shield, which gives me a UK IP address so I can watch episodes online if I want, and episodes of Doctor Who Confidential, which does not come on BBCA. Simon Pegg narrated the first series of that show (he also appeared as the Editor in the 7th episode of Eccleston's run).