quirkiest This is the correct option.
All three of them are a little off, but Shavonne is the quirkiest
The speaker is giving an opinion about three persons. The three of them seem to be funny or strange but there is one among the three, Shavonne, who seems to be the funniest or strangest, so the superlative of the adjective quirky is neeeded to describe her.
These options are not right:
-quirky: One person is quirky
-quirkier: One person is quirkier than the other. We are comparing two persons.
