The correct answers are to study medicine; adverb.
Infinitive phrases are relatively easy to spot - they begin with the word to, are followed by the main verb, and the rest of the words closely connected in meaning. In the example above, the infinitive phrase is to study medicine - we have the word to, the verb study, and the object medicine. (Even though the phrase to college also begins with to, college is not a verb but rather a noun - this is a prepositional phrase).
The use of the infinitive phrase is adverbial - it means that it can tell us the time, place, manner, etc. of the verb, of the action being performed. In the example above, we see the reason why Candice went to college.
