Wolfenstein: Enemy Territory

It may not look particularly unique among other shooters from that era but where this game really did things differently was that unlike most multiplayer modes of those shooters, Enemy Territory has what I consider to be the perfect blend of arena shooter chaos and more realistic, objective-based combat.

Simple mechanics - easy to learn, well balanced, simple but meaty weapons choice.

First, this game won't work right out of the box, you need to install ET Legacy, not only does it revive the master server list, but it also brings many QoL improvements like a proper Alt+Tab command (the original famously didn't have such a thing), higher resolution and framerate support, better audio and many more MUCH needed improvements.

all weapons and classes are balanced, except adrenaline (but many servers either remove it or limit its use)

While the visuals are modest by modern standards, the clarity of design supports competitive play.