Lost to the Zone (basic Anomaly storyline): Available at your faction leader in your starting base with these factions: Loner / Clear Sky / Duty / Freedom / Mercs / Ecologists
Mystery of the Zone: Loner / Clear Sky / Duty / Freedom / Mercs / Ecologists
Mission Afterglow: Available at the start of the UNISG playthrough (type isg in character creation menu to unlock this faction).
Artefacts Hunters: To start the plot, you need to go to any NPC from among the "Artifact Hunters" (for example, Kovalev in the church in the swamps) or find their representative, a stalker-ecologist named Sarik the Twilight in the village of newcomers. Available to Ecologists allies: Loner / Clear Sky / Duty / Freedom / Military / Mercs / Ecologists
Last Dawn: Talk to Spore in the Swamp Clear Sky base. Available to Clear Sky allies: Clear Sky / Loner / Freedom / Duty / Mercs / Ecologists
Operation Monolith Retribution: Talk to Colonel Kuznetsov and help the military take control of the very Center of the Zone! Available to Military allies: Military / Ecologists
Dr.X questline: Available to all factions, not really story oriented.