Over time in the Zone, stalkers formed groups, affiliations and networks, here called factions for ease.
The most common faction, and the oldest one, was the lack of one! Making allies and friends in the Zone was a hard task, so why put in such efforts?
As the biggest "faction", free stalkers came in all ages and level of skill, but most fit into one of two stereotypes. Most factionless were either unexperienced rookies who had just entered the Zone, or grizzled veterans who made an effort to not ally themselves with anyone else for whatever reason.
The biggest and oldest ACTUAL faction.
When Pauchok came to power, he started trading with criminal organisations.
As the name tells you, this faction was made up of soldiers for hire. They did most anything for money, from scouting unknown land and doing construction work, to dangerous artifact hunting and assassinations.
A small and humble group led by the scientist Kirill Kaluzha.
The members were the Kaluzha family and a few other stalkers trusted by Kirill.
This was a small, short-lived, radical group and, accoring to some, cult. The members were all mutated or otherwise affected by the Zone in some way, either from being children of stalkers or through accidents with anomalies.
They believed they were the rightful owners of the Zone, as they were the "children of the Zone". Even though the group only lasted for a few years, CotZ managed to have two different leaders, with very different views on their mutated existence.
The first leader was named "Pushek", a young and incited man. He believed it was unjust that he and his mutated comrades, after being so horribly deformed by the Zone, got nothing but hatred, disgust and abuse in return. He demanded the Zone would fundamentally belong to mutants, and that all non-mutants were taking from their land.
Not really a faction
(I wish I knew enough about the Russian military complex to make an accurate name for the specific military group tasked with controlling trespassing and smuggling in the Zone, but I don't, so they are just called Spetsnaz. If you know anything about such things, please e-mail me and explain it in layman's terms, because wikipedia does not make it easy for me...)