In Fahrenheit 451, what was man's major pursuit during Montag's time?
In Montag's time, man's pursuit was to find momentary happiness without depth. This is demonstrated through the types of classes offered at Clarisse's school, the fact that the society burned books which would challenge a person to think, and the false interaction Mildred had with the "family" of characters that invaded their living room on a daily basis.
If by chance, you are referring to the era in which Ray Bradbury wrote the novel, then the 50s were influenced by man's pursuit to tell on other men who were in the wrong. Book burnings, censorship, and ill-treatment of any Communist friendlies all became commonplace.
All things trivial and distracting were the primary occupations for the members of the futuristic society in which Montag lives. From watching live, interactive, mindless television on wall sized televisions to driving 200 miles an hour just for kicks, Montag's society is wholly focused on the immediate gratification of the senses. Much like Huxley's Brave New World, Bradbury's goal was to provide readers with a cautionary tale about the dangers of mindless entertainment and its ability to distract us, literally, into destruction.