During despotism, only build improvements that are absolutely necessary. I generally try to get to republic before my total maintenance costs exceed five per turn. (Usually one granary, one barracks and three temples or two temples and a harbor). You just don't make enough money in despotism to afford many improvements without having your research rate suffer because of it. Republic makes more money than monarchy so if you're not warmongering go for Republic. It also doesn't hurt to use taxcollectors or scientists in cities that would be in disorder otherwise. After you get republic, build as many libraries as fast as you can. That should help with research. Then build as many marketplaces as you can. That will increase each city's commerce by (50% I think).