Good, non-busy time is a weekday when school's in session, morning (I'd get there before 10.30am). With that, I would think the wait for the ticket should be 5-15min and then you should be able to get on the elevator pretty much right away. It's also popular to go there right before sunset, but it'll be busier then.

Of course, there's almost no sense in going if it's not a clear day. You have the best chances for a clear view during winter.

Tokyo Sky Tree is the best out of the towers imo. I think it's well-positioned for a very nice view of Tokyo skyline with potentially Mt.Fuji in the background. It's got an extensive shopping/dining complex below that's an attraction in its own right, although I personally don't like the layout and I think there're definitely better shopping complexes elsewhere. I did have possibly the best maccha latte I've ever had, though.