Should they get married while he is visiting and apply for adjustment of status or should she get him a K visa and then adjust his status?

There are advantages and disadvantages for each of the options you mentioned, beyond what can be discussed in a response that is just a few sentences long. Beyond that, there are legal issues relating to timing: a visitor's visa is exclusively for someone entering the U.S. with "nonimmigrant intent," i.e., an intention to remain temporarily in the U.S. and then depart. It is not lawful to enter with a visitor's visa with the intention of becoming married and then applying to remain permanently as a Permanent Resident (with a "Green Card"). Misuse of a visitor's visa can constitute visa fraud, with very serious immigration-related consequences. Nonetheless, it can be lawful to enter with nonimmigrant intent, and later have a change of mind and decide to become married and apply for Permanent Residency. There really is no substitute for your daughter and the man she is considering marrying to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain the couple's goals, and who then could offer legal representation in the often complex application process.