Xonotic [0] is an amazing game if you're into quake style arena shooters. It's a fast paced multiplayer shooter and like 0 A. D. also OSS.
Easiest to get up to speed in the "minstagib" or "instagib" mode, where basically one shot kills and "bullets" arrive at their target instantly. Once you're familiar with the mechanics, the other modes are quite fun, too.
Just remember that the free to play model is about using tricks to encourage you to spend money, usually with shitty game mechanics unless you pay. If you are not going to pay on a multi-player game, your role is to improve the user experience for other players that are actually spending money. To replace an AI, so they spend more.
So I would skip the free to play games if you don't have a budget for them.
My personal favorite free and open-source game is OpenTTD but it's a bit dated.
If you're willing to shell out $6, I can't recommend Sid Meier's Alpha Centauri enough, especially if you're into turn-based civ games. GoG has a ton of older stuff for less than a Hamilton. https://www.gog.com/game/sid_meiers_alpha_centauri
I have been playing a lot of Mindustry lately, not just free, the game is open source too.
"Mindustry is a hybrid tower-defense sandbox factory game. Create elaborate supply chains of conveyor belts to feed ammo into your turrets, produce materials to use for building, and defend your structures from waves of enemies. Features include a map editor, 24 built-in maps, cross-platform multiplayer and large-scale PvP unit battles."
itch is oozing with free-to-download or pay-optional games by hobbyist and new game developers. I'm a big fan of it. Some of the stuff is very raw though, compared to Steam or Epic pages being more product-oriented.
I don't think my picks will be similar to 0 A.D., but some interesting ones that stick out to me are:
Edit: also GOG: https://www.gog.com/partner/stay_at_home