Should he be living and working for a certain amount of time before I can marry him and apply to adjust my status?

Significantly more information is needed in order to provide a legal analysis of ways you can achieve your immigration-related goals. Note that entry into the U.S. through the visa waiver program, through a visitor's visa and through many other types of visas requires "nonimmigrant intent," i.e. an intention to enter only temporarily in compliance with the program or visa, and an intention then to depart. If your intention is to enter the U.S. in order to adjust status to become a permanent resident based upon your marriage to a U.S. citizen, then you would not have "nonimmigrant intent." Misusing the visa waiver program or a nonimmigrant visa can present risks of being found to have committed visa fraud, with very harsh consequences. Generally a U.S. citizen may sponsor a spouse to become a Permanent Resident without regard to the amount of time the U.S. citizen has lived and worked in the U.S. There are many other details that address eligibility, and it would be wise for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.