How important is knowing and memorizing the Quran and Hadeeth and the jurisprudence related to Hadeeth and the Quran for a caller to Islam?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

It is the duty of whoever conducts Da‘wah (Islamic propagation) and encourages good and forbids wrong, to be equipped with knowledge about the field he is calling to so that he may invite to Allaah The Almighty with insight. Allaah The Almighty Says (what means): {Say, "This is my way; I invite to Allaah with insight, I and those who follow me. And exalted is Allaah; and I am not of those who associate others with Him."} [Quran 12:108] 

No doubt, the worthiest thing to be learnt is the Quran. Allaah The Almighty Says in this regard (what means): {Rather, the Quran is distinct verses [preserved] within the breasts of those who have been given knowledge. And none rejects Our verses except the wrongdoers.} [Quran 29:49]

The Sunnah explains the Quran, and that is why a person has to memorize as much as he can of that as well.

In addition to memorizing the Quran and studying the Sunnah, the jurisprudence related to Hadeeths should also be learnt. The Prophet, sallallaahu ‘alayhi wa sallam,  highlighted the importance of knowing the jurisprudence of Sharee'ah texts in the Hadeeth which explains that a bearer of knowledge may not be a scholar of jurisprudence and his student may be more knowledgeable than him. [Ibn Maajah and Al-Albaani :Saheeh (Authentic) ] Ibn ‘Adiyy narrated that Al-'A‘mash, a prominent scholar of Hadeeth, told Abu Haneefah that the scholars of jurisprudence are like physicians, while the scholars of Hadeeth are like pharmacists. The same was said by Yahyaa ibn Ma‘een to Abu Thawr, as stated by Ar-Ramahurmuzi all.

Allaah Knows best.