What are the Quranic chapters that are recommended to be read first by non-Muslims in general, and the People of the Book in particular, when calling them 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 ‘alayhi wa sallam, is His slave and messenger.

We found no particular Quranic chapters that are recommended to be read by the People of the Book or other non-Muslims.  However, if someone is interested to learn about Islam he should first read the verses speaking about Islamic monotheism and the Oneness of Allaah The Exalted. For example, he could read chapter Al-Ikhlaas (chapter 112 of Quran).  Islamic monotheism was the basis of the Da‘wah of all the Prophets, may Allaah exalt their mention, as proved by the verse in which Allaah Says (what means): {And We sent not before you any messenger except that We revealed to him that, "There is no deity except Me, so worship Me."}[Quran 21:25]

Additionally, Allaah commanded the Prophet, sallallaahu ‘alayhi wa sallam, when arguing with the People of the Book, to begin by calling them to acknowledge the Oneness of Allaah The Exalted.  Allaah  Says (what means): {Say, "O People of the Scripture, come to a word that is equitable between us and you - that we will not worship except Allah and not associate anything with Him and not take one another as lords instead of Allah ." But if they turn away, then say, "Bear witness that we are Muslims [submitting to Him]."}[Quran 3:64]

Reading the verses speaking about the wisdom and purpose behind the creation of mankind is also important. Almighty Says (what means): 

The verses speaking about the power and might of Allaah The Exalted, and the fabulous creation of the universe, including the heavens and earths, together with the verses that explain the consequences of disbelieving in Allaah and what He The Almighty has in store for the disbelievers are also important to be read by non-Muslims.  The chapter of Fussilat (chapter 41 of Quran) covers all these matters. 

That is why the Prophet, sallallaahu ‘alayhi wa sallam, recited the opening verses of this chapter to ‘Utbah ibn Rabee‘ah (a disbeliever) until he reached the verse in which Allaah The Almighty Says (what means): {But if they turn away, then say, "I have warned you of a thunderbolt like the thunderbolt [that struck] ‘Aad and Thamood.}[Quran 41:13] After hearing these verses, ‘Utbah was strongly affected by the Quran and returned to his people praising its eloquence and the articulate nature of its language. [Al-Haakim, Abu Ya‘laa and Ibn Abi Shaybah]

The People of the Book should also know the true creed concerning 'Eesa (Jesus) .  This was mentioned in different chapters of Quran such as Aal ‘Imraan, An-Nisaa’ and Maryam. In brief, the whole of the Quran is a Book intended for Da‘wah, guidance and light, therefore, every Muslim should use it (or the translation of its meanings) to call non-Muslims to Islam.

Allaah Knows best.