Yeah, maintenance really starts to kill on emperor.
I don't think "number of games" is the right question? In order to move up, you should reach a comfort level with your current difficulty level and achieve consistently better success with each victory condition and map. I would try winning at least one of culture, space, and dom/conq as the usually involve significantly different strategies and test all your skills. Furthermore, I think you should start achieving earlier victories - like say pre-1900s(except from maybe space)
With that said though, as you are playing and enjoying your current level, I think it's fine to try out harder games like those in some of the series run on the board for at least the learning experience and advice you get from others. Emperor Cookbook is a good option. I believe one is starting this week.