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 people who are extremely enthusiastic or devoted to a cause or group, which fits the context of fans who go to great lengths to support their team.
Here’s a brief overview of the other options:
- Fatuous means silly or foolish, which doesn't fit the context.
- Flagrant means conspicuously and outrageously bad or reprehensible, which also does not fit here.
- Feline relates to cats, and is irrelevant in this context.
Therefore, fanatical is the most appropriate choice.