Dungeons and Dragons

Check out Disboard, and search for 5e or avrae (and optionally play by post) to find a discord server to play on.

There are plenty of small Discord servers that use a bot called Avrae to automate the crunchy mechanics of d&d 5e, with things like char sheets, initiative, monsters and combat, and even maps. Some servers are slow paced, where everyone is expected to act once per ~24 hours, so you get a nice asynchronous game going where you have time to learn your character's abilities, bot commands, etc, all while typing up your roleplay that matches the mechanics of your turn. That format is great for learning and getting the hang of things in the system, IMO, because you have a ton of time to ask questions in a chat channel to have others help you. Other servers will do sync events, where you sign up for an event with a specific star time, hop into a voice channel, and play with ~5 minute turn timers to really crunch through some combat quickly. This is great once you have the basics of Avrae down (and by extension, the mechanica of 5e).

That's usually a "westmarches" format, where the server has a large number of players who queue up for events, but each event can only accommodate a small number of players from the top of the queue. You get grouped with random others this way (contrast that to "campaign" play where you stay with the same players for many consecutive sessions). IMO westmarches really helps get you acclimated to D&D through broad exposure to lots of classes, monsters, mechanics, RP styles, etc. And it works really well for someone who is casual!