Here is a set of links to good sites:
Where to play?
lichess.org - One of the largest sites for playing western chess (and some western chess variants) online. Completely free and open-source, and with excellent diagram, study and analysis tools.
pychess.org - With a powerful backend based on Fairy-Stockfish and an interface based on lichess.org, PyChess offers many different kinds of chess. Established games like xiangqi, shogi, janggi and makruk; western chess derivatives like S-chess and Grand chess; hybrids like Shako and Shogun; many games await you here. Play against a Random-Mover bot, or face off against different levels of Fairy-Stockfish in any of the variants. Or perhaps even play against other humans!
playok.com - Originally a Polish website, PlayOK has gained a large following among South-East Asian players for their local favourites of makruk and xiangqi. Western chess, backgammon, weiqi/go/baduk, shogi, gin rummy and reversi are among the many other games you can play here.
Who can I discuss with?
PyChess Players Discord Server - A Discord server for the players of PyChess. There are channels dedicated to each of their many variants, and developer discussion is frequent as the site continually improves and expands. Join also to participate in Showcase Sundays, where each week a different variant is featured and several games are streamed.
The House Discord Server - A Discord server for many chess variants, including atomic, crazyhouse, bughouse, antichess (losing chess), 4-player, Horde and much more. A lively community including many strong players in each variant, some of whom are even GMs and IMs in regular chess.
My other site
Ars Atomica - My website focusing on atomic chess, with instructive articles and content, as well as links pointing to my other instructional resources on lichess.