How can a woman decide whether a person who proposed to her is suitable or not? Assalam Alaikum

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

There is no common stand of the jurists regarding the suitability in marriage. But the majority of scholars believe that it is a condition in marriage and a right for the woman and her Wali (guardian). But the scholars differ about suitability.

1) The Hanafi School of jurisprudence are of the view that suitability is defined according to the lineage of the person, his state (slave or free), his wealth, his religion and his profession.

2) The Maaliki School of jurisprudence are of the view that suitability in marriage is realized in two things: the religion and the safety from the defects that give the woman the right to choose between staying married or getting divorced.

3) The Shaafi’i School of jurisprudence are of the view that the suitability lies in the fitness of the man; i.e., being safe from all the shortcomings that give the woman the right to choose between continuing in conjugal life or divorce. They add to this, the man's state (slave or fee), lineage, religion, piety and profession.

4) For the Hanbali School of jurisprudence, this suitability lies in the religion, the lineage, the profession, and the wealth.
Anyway, the woman has been given by the Sharee’ah the right to refuse any man she does not feel to be a good match for her. Probably, the Maaliki’s point of view which considers the religion and the safety from defects as the only criteria for suitability is the most suitable for people these days. This is to make marriage easier and close the doors of temptations. This is backed by the Hadeeth reported by Ibn Maajah that the Prophet said: “If a man whose religion and moral conduct are pleasing to you proposes to you, then let him marry; otherwise there will be great mischief and corruption on earth.” [At-Tirmithi]

Allah knows best.