The favored game of 30 year old boomers everywhere, Quake is probably the most well-known Arena Shooter. Featuring fast paced gameplay, it has been a mainstay of esports for decades, though not as well known these days. It still commands a small yet dedicated playerbase.
There are five games in the series, though I've only played Quake 1, Quake III Arena/Quake Live and Quake Champions. Quake III is probably the best among the series.
Quake I Singleplayer, bonus map.
Quake III Multiplayer, railgunning.
Quake III Multiplayer, about to get blasted.
Everything right and wrong with Quake Champions.
Movement is the mainstay of the Quake series. Do learn how to rocket jump, strafejump, circlestrafe, and other movement tricks.
With the exception of Quake Champions and possibly Quake IV, most of the games here will be able to run on a computer capable of running a modern OS.
Quake I to III have been released under the GNU GPL License, meaning they are free software as defined by Stallman. However, the content (maps, art assets, sounds, etc.) are still copyrighted, meaning you still need them if you want to play a free source port.