These are many purans, 18 being main. A brief history by Shivoham Project can be watched.

One way to classify these: (a) those that narrate stories that look fictious but convey essential teachings of Veds/ Upanishads  and (b) those which describe Itihaas [history].

Another way to categorize these: Three sets, each connected to one of the trimurti – Vishnu, Brahma and Shiv. 

There are other purans over and above, which are also listed in the table below.

One observation: In puranas [specially non-historical ones], the question is asked by Brahman and answer is given by Soot[सूत]. This indicates that in puranic timeframe, soot was not a lower caste. You can read more about these at (a) The Divine Life Society site, (b)Hind Utsav site

Vishnu Brahma Shiv
Narad Bhavishya Ling
Vaman Agni Kurma
Garud Brahmavaivarta Markandey
Matsy Brahmand Skand
Srimad Bhagawatam Padm Varah