It's actually S1 that's my worst deficiency--I haven't seen any of it

You should definitely watch it as soon as possible, it's a brilliant series. If you don't get a chance to watch it all, at least watch The Empty Child/The Doctor Dances. It's the introduction of Captain Jack and 2 of my favourite episode of the entire show! (Especially if you like Moffat's writing, it's wonderfully creepy)