The four qualities a Receiver (or Giver) must have are intelligence, integrity, courage, and wisdom.
When the Chief Elder announces Jonas' selection as the next Receiver of Memory, she mentions the four qualities a Receiver is supposed to have. First, he must be intelligent; Jonas fits the bill because he has been a good student during his school days.
Second, the Giver must have integrity. The Chief Elder mentions that she's very proud of Jonas for being honest about transgressions and presenting himself promptly for chastisement when they happen. Third, a Giver must be courageous, and the Chief Elder tells Jonas that he's inspired her to believe in his courage. She informs him that he will have to experience extreme pain during his training, but reassures him that she trusts in his courage to endure.
Fourth, a Giver must be wise. The Chief Elder asserts that Jonas has not yet acquired the wisdom he will need for his position. However, she is confident that he has the capacity to acquire the necessary wisdom during his training.
Altogether, these four qualities encapsulate everything that a Giver needs to be successful in his position. The Chief Elder does mention one last quality, the Capacity To See Beyond, a quality she cannot easily define but which the present Giver tells her that Jonas is equipped with.