There are actually 5 qualifications for being the next Receiver of Memory. 4 of those 5 are outwardly visible to people in the community. The fifth can be named, but not really described.
The first four qualifications are specifically named by the chief elder. They are (in no particular order):
Wisdom. Technically Jonas doesn't have much of this when he is chosen to be the new Receiver, but the chief elder does say that Jonas "has the ability to acquire wisdom."
Intelligence. Jonas has demonstrated to his teachers, the elders, and the community that he has been a "top student throughout his school days."
Courage. Jonas will need his courage as he receives his training, because he will be subjected to a great deal of pain. The chief elder and the current Receiver both "feel certain that you [Jonas] are brave."
Integrity. Like any other member of the community, Jonas has committed errors and mistakes. Jonas displayed his integrity by always "presenting himself promptly for chastisement" when he had done wrong.
The fifth qualification is called the "Capacity to See Beyond." The current Receiver has already verified that Jonas has the ability. Concrete evidence of Jonas having this qualification is his ability to see colors.