I'm not opposed to a female Doctor, I think so many liberties have been taken in the RTD era (last of his kind, wiped out the daleks until we fancy a dalek story line etc) that complaining about cannon at this point is daft. Basically the "doctor is male" cannon, only exists until the doctor is female, at which point it will definately be cannon that the doctor can be either.
The actor I'd most like to see do this part is Mark Williams (Mr Weasley), I think he is brilliant at the enthusiatic geeky interest in muggles humans thing. He'd make a refreshing change too. However other than that preference I'd be happy to see a woman and/or a person of colour in the role.
Some better writing (leave out the deus ex macheina, the extraordinary talents of companions, the ridiculous wiping out of entire species only to have to have more and more implausible reasons for their return) and a focus on storylines would be great, along with companions who don't have a sexual attraction to the doctor (that's pretty boring now) - i know some male companions have been pointed out, but it might be nice to have the doctor travel with a male companion for a while, rather than the rory and mickey situation where they were adjuncts to the female companion. maybe an older person would be good. bascially more variety, what about a child/teen additional companion for a bit?
i'm disappointed that from what you are saying Moffat is reponsible for the dire writing of women, as i didn't get on with RTD and had high hopes when moffat took over as some of the best episodes for monsters/ideas for scary stories during rtd's time were moffat's (Weeping angels, vashta nerada). Apparently you can't have everything.
dh (a fan of the original Dr. who) isn't as keen as i am on having a female doctor as as others on here have stated if he was going to regenerate into a woman, he'd have likely done it by now rather than being a man for so long. But then there are a lot of things he's not keen on with the new series - the one episode stories etc- so i don't think it would be a deal breaker for him. however he would like to see a man of colour in the role, and also likes the idea of a spin off series about a female timelord in the whoniverse with cross over episodes.
Due to john hurt potentially being the Valeyard, I suppose it will be less likely we'll also get an older doctor.