I personally like the first Doctor in the first season. although, I hate Rose. I think that she is a dumb blonde. Although the Second Doctor was OK, he just didn't seem like a Doctor if you know what I mean. I feel bad saying it though because he did brilliantly in Harry Potter.
I'm still in that phase where I'm obsessed with my first doctor, who is also the latest doctor (Matt Smith). I've watched a few David Tennant episodes and he's growing on me, but I'm still married to the Ponds, bow ties, and fish fingers and custard.
I have not seen any of the old series (I do plan on watching them). My favorite Doctor from the new series is David Tennant (but the very very close is Matt Smith). *Spoilers for the rest of this* (if that's even necessary) His transition when he was leaving was, by far the saddest.. "I don't want to go." Tears everywhere!
My favorite Companion is Rose. She went to great lengths for him and the story was definitely the saddest.
My least favorite is probably Amy. The story is good with her, but as a character, she really irks me. Rory loves her SO much (2,000 years. just saying) but her affection comes nowhere near his. However, this could lead to a theme of sorts. I know I have a fear of not outwardly reciprocating affection to my boyfriend. Either that or this could just say something about her personality (or I'm over-judgmental because she tried to shag the Doctor).
I know that Rose had a bit of the same issue that Amy had with kind of ignoring Micky, but he was just a boyfriend (as opposed to a fiance or husband), he didn't do as much for her, and his character isn't as likable (and I am probably biased).
I agree- the David Tennant/Rose combo will always be my favourite!
From the Old Series, Tom Baker was my favorite Doctor, although his decision to not appear in The Five Doctors was pretty disappointing.
David Tennant is my favorite New Series Doctor. My favorite episodes of his are as follows
-The End of Time
I really like The Empty Child for Eccleston, and A Good Man Goes to War and Amy's Choice were great for Smith.