I grew up with Pertwee/Baker so they'll always be my favourites just out of unabashed nostalgia : )
Of the new bunch I liked Ecclestone the best by far, just because I rate him so highly as an actor besides which it was great to see the Doctor back on telly. I've not really kept up with it since then though I did make a point of watching the Gaiman episode.
Villains is tough, there have been so many! Daleks, obviously. Especially when they started flying. I remember the Sontarans being pretty frightening when I first saw them (about 7 years old at the time I think). I reckon on the whole though my favourites were the Sea Devils, I seem to remember them in a series set in some Scottish castle or other with Jon Pertwee. Happy days : )
Oh yeah, the giant maggots! Anyone remember those?
Companions/others - I liked Rose a lot (slight Billy Piper crush lol) but what I remember is always being really chuffed when the Brigadier popped up.