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I just recommended it in another thread but Battle for Wesnoth is a free open source strategy game that has you vying for control of villages on a map with the goal of having enough forces to tactically kill your opponent's leader. Each of the various fantasy factions of the game starts with a fairly straightfoward set of units with dedicated roles (e.g. Elvish Archers are ranged units, Elvish Shamans heal, Merfolk are dedicated water units, etc...) but can promote if they gain enough experience from kills to become better at their role or take on a different role entirely. This combined with the RPS dynamic of different unit interactions means that battles that look fairly simple on the surface can become complex fights that encourage you to check things like unit positioning, terrain, what damage types your unit can deal, the time of day, etc... to outwit your opponent. There's at least 6-7 story campaigns with multiple difficulty levels that can help ease you into the game; I'd probably recommend a shorter easier one like A Tale of Two Brothers that could be completed in a few sessions.
You might be interested in looking into a few Minecraft clones if price is a concern - Minetest is the most well known one from what I've heard but I was recommended Terasology a few years back.
Lastly there's XMage which allows for PVP with rules enforcement. It's a bit resource intensive though, so I would probably try the other two first if you're interested.
Cockatrice is a nice small lightweight tabletop option that lets you install it, load in a deck, register+join the server, and play. No rules enforcement though so you'd probably want to have a few simple decks and some basic knowledge of the game