Helena Bonham Carter would be a fantastic Doctor. Helen Mirren would be pretty awesome too, but she might be considered a bit too old to follow Capaldi... I would also like to put Natalie Dormer up for nomination.
As for RTD, he did a good job of bringing back the series, but during his run Moffat's episodes were consistently the best ones and I think the man has done a great job throughout his run of the series. I want more episodes written by Neil Gaiman, myself. Maybe he should be the one to take over after Moffat?
Not so. The sonic screwdriver made its first appearance in 1968, during Patrick Troughton's tenure.
Of Classic Who I liked Jon Pertwee and Colin Baker the best, to be honest. Since it started up again I've been fickle. I loved Eccleston so much and pretty much flew into a rage when he went away, but then I got to know Tennant's Doctor and thought he was the best thing ever and no Doctor would ever be as good as him, and then came Matt and I hated him and then I loved him within the first two minutes of The Eleventh Hour. By fishfingers and custard I was utterly sold. (It was sort of like when Daniel Craig was cast as Bond, and I saw a picture and was like, wtf is this he looks like a Bond villain and didn't watch his movies, and then I caved and saw Skyfall because of Ben Wishaw and now Craig is the only true Bond for me even though I loved Sean Connery since I was like 8.)