Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
Who should be invited?
Sayyiduna Abu Huraira (Allah be pleased with him) states: �The worst food is that of a wedding banquet (walima) to which only the rich are invited whilst the poor are not invited. And he who refuses an invitation (to a banquet) disobeys Allah and His Messenger (Allah bless him & give him peace).� (Sahih al-Bukhari, no. 4882)
It is stated in al-Fatawa al-Hindiyya:
�It is recommended to invite neighbours, relatives and friends.� (5/343)
Thus, one should invite family-members, relatives, friends, associates, scholars and pious people and others. It is wrong to invite only rich people or those who are regarded to be from the upper-class. Also, concerning a non-Muslim there is no problem, and it should be remembered that any interaction with non-Muslims is within the guidelines of Shari'ah.