The word that best completes the sentence is "fanatical."
The completed sentence would read: "Some of the team's fans were fanatical and spent incredible amounts of time and money following them around the country."
"Fanatical" describes an excessive enthusiasm or devotion, especially in the context of sports fans. The other options do not fit the context as well:
- "Fatuous" means silly or foolish.
- "Feline" pertains to cats.
- "Flagrant" means obviously offensive or disgraceful.
Thus, "fanatical" is the most appropriate choice.