CS:GO is also an FPS and is massivley big on the competitive scene. For a great experience with friends, I really recommend it.

HL2 is the take on from HL1. It has an amazing story line, great graphics for it's time, and if you don't have it already it's an essential steam game.

GMod is definitley the best modded sandbox community game. There are heaps of servers with many different gamemodes. Just spend $10 and buy it already!

This game is literally the most amazing and enjoyable f2p fps. From the hats to the gamemodes, it's amazing. I really recommend it.