I had a pretty similar reaction to DW. Thought it was silly fun at first, but the more episodes I watched the more I enjoyed it. And then upon rewatch of season one, I realized that the first few episodes are actually some of my favourite ever. Weird. I also had a similar reaction to David Tennant. Didn't think he could pull off the dark stuff like Eccleston. But he definitely grew on me.

PS Barrowman's American accent is real. He grew up in the States.