Answer
Bromthymol blue is the best choice for that titration, because the pH of the equivalence point is equal to 7.00, and this indicator changes its color between pH = 6 and pH = 8.
Work Step by Step
$NaOH$ is a strong base and $HClO_4$ is a strong acid; therefore, the pH at the equivalence point is neutral $(pH = 7.00)$.
As we can see on page 667, the Bromthymol changes its color between the pH values 6 and 8, so, it is the best choice.
