Absolutely.
I started watching with Colin Baker and Sylvester McCoy, so unfortunately they were my earliest memories of the show. But discovering the earlier Drs, paricularly Tom Baker has been great.
So
Favourite Dr: (Old Series) Tom Baker, (New Series) Not sure, i liked early Matt Smith a lot more than later.
Favourite Story: Hmmm Probably (Old) Talons of Weng Chiang (New) Blink or The Beast Below
Favourite Companion: (Old) Leela (New) Martha maybe by dint of ultimately not making a bad impression on me.