What type of sugar can preserve bread the longest?
I don't think a spoonful of sugar, honey, etc added to a loaf to encourage the yeast will make much of a difference. Sugar can act as a preservative but only at pretty high concentrations, and the amount you use in bread isn't going to be high enough.

My experience is that home-made bread will get stale long before it gets moldy. I've seen supermarket bread go moldy but I assume that's because they use some pretty serious preservatives that means the bread has the time to develop the microbes - say, a week or more.  

I'm thinking about cake, which is pretty much a ultra-sugary bread, and even the amount of sugar there isn't enough to avoid it going stale. And again, that goes stale faster than it goes moldy, at least here in the cold North of England.