What memories does the Giver want Jonas to remember?

As readers come to know the Giver, we realize that he is a kind and loving individual. He genuinely cares for Jonas and the community. I'm quite certain he wants Jonas to only remember the happy and good memories; however, the Giver also wants Jonas to understand that true happiness can only be fully understood when it is compared to other more painful memories. The Giver wants Jonas to have that understanding even though the Giver knows it will be painful for Jonas.

"It hurt a lot," Jonas said, "but I'm glad you gave it to me. It was interesting. And now I understand better. What it meant, that there would be pain."

If the question is asking about what memories the Giver wants to give Jonas to meet the requirements of the Giver and Receiver of Memory relationship, then the Giver "wants" to give Jonas a memory of everything. The Giver is getting old, and the community still recognizes the need for a person to have all of those memories. Jonas is chosen, so the Giver is supposed to pass on everything to fulfill his duty and get Jonas as ready as possible. It was done to him, and now it is Jonas's turn.

There's much more. There's all that goes beyond—all that is Elsewhere—and all that goes back, and back, and back. I received all of those, when I was selected.