So I've been watching the series to see the episodes I never saw and stuff, just the New Who stuff, and I just finished Eccleston's run and the first Tennant episode last night.
So here are my thoughts on that: the first few episodes make it clear that the whole staff is trying very hard to find the show's footing. Things are a wee bit wonky, so to speak, and characters are not exactly set in stone. Eventually things pan out a bit better by the end of the season, though.
In terms of episodes, I'd say that the best ones were Father's Day and The Empty Child. Boom Town was going really well, but I was severely disappointed that the writers copped out and made the villain do something evil that got her killed automatically, rather than actually have the Doctor cope with sentencing an enemy to death after dining with them. The Empty Child was great, though, because it was Sci-Fi Horror and honestly those weird Sci-Fi Horror episodes are the best part of Doctor Who for me.
Nine and Rose's relationship has a lot of creepy, abusive undertones going on, not helped by the fact that Nine is a jerk and pretty racist to boot (by which I mean his constantly calling Rose things like Stupid Ape.) This is really clear during the Father's Day episode when they have an argument and she's like "you'll be back, you always come back" and all that. Really unhealthy relationship they have going on, especially since the Doctor uses the "Get in my damn TARDIS now or I am leaving you here forever" bit on her multiple times. Makes me pretty concerned that so many young women treat this relationship as the best one in the show, but then maybe it is Rose and Tennant they look at, I dunno.
I'm not a big fan of Rose. During Eccleston's run she wasn't too bad, but I really disliked how she ditches Mickey and then keeps using him every time she pops up in the present again. Mickey I'm split on because his reactions to her abuse are great, but his never ever leaving her sorry ass is hard to watch. Anyway, she was fairly tolerable until the Christmas Invasion, when she's somehow mad at the Doctor for regenerating. Dude takes a bullet for her and she's mad at him, and all throughout the episode she waivers between whining about how she can't do crap without him and how awful and normal life is without him. Girl tells Mickey "There's nothing here for me now." Except, you know, YOUR MOTHER. I don't know, I don't think Billie Piper's performance is off, I just think Rose is a poorly written character, a fairly flat love interest, and a much weaker companion than basically all of her successors, who were very proactive women.
Daleks were sick as heck. Their episodes always had an "OH DANG STUFF IS GONNA HAPPEN" feeling to them that really sells you on the fact that these trash cans are competent foes.
I enjoyed Nine. He was much more open about his jerkass side than Ten and Eleven, who are fairly cheery guys until SUDDENLY SERIOUS from what I remember. I do think his regeneration is perhaps the least dramatic of the ones I've seen, but then, with only two that's not exactly a whole lot to say.
Captain Jack was kind of meh, but then I feel that's influenced by the fact that I did watch all of Torchwood and the longer that show went the worse his character got. Harriet Jones is pretty great, though, and Rose's mom is a good comic relief.