seconding warframe for firefall-likes. if you decide to try it, look up the wiki. the game's fairly grindy, but recently i've found the rng to be pretty ok because the amount of different drops you get from one specific source is usually pretty limited. other than that, for syndicates you should level either [steel meridian and cephalon suda] or [red veil and new loka]; favoring the first in each pair. doing either of those gives you four syndicates out of six, and all of the syndicates have nice items without too much rng. also, there is an /unstuck command and you will need it. also, there's a lot of ability and equipment variety once you get started, which alleviates the grind.
card games!
duelyst is good, and pretty newbie-friendly. think hearthstone on a chessboard. i only started recently, but play more than my daily quests.
infinity wars has a neat concept and base rules, but you end up playing premade decks and there are long waiting times.
dungeon crawlers!
dungeon crawl: stone soup has great gameplay mechanics and no plot. it has the best gods and god-powers. it has a god that lets you be the jesus of orcs, one that turns you into a tornado, one likes slow things and makes you slow and strong, and one that asks you to sacrifice parts of your character for power. also class gods and good(restriction) gods. it's a game i keep coming back to even though i've never come far in it.
elona is fucking weird. its gods give you items and stat-boosts, and are all over-the-top anime archetypes. extremely wiki-dependent.
adom has a plot and quests and stuff, but i didn't like it. it has the most boring religion system.
platformers!
starbreak is an mmo-roguelike-bullethell-platformer, which is fucking weird. i played it a lot for a short time, then burned out after unlocking all the classes and hardly played it since. there are no character-slots without microtransactions, which means you get stuck playing the same class until you die without a lot of variation to the gameplay. all the classes play very differently, though. once you think you can unlock duskwing when you die, don't. try to live until you unlock ironclad.
khimera: destroy all monster girls is a beat-em-up platformer with a megaman-esque progression system. it has some difficulty-curve problems and i laughed far more seldom than the game tried, but it's fun enough to complete.
cave story is a classic run and gun platformer with somewhat floaty handling, the weapons and enemies are both neat.
superfighters deluxe is a pvp platform shooter with an action-movie theme. it has flamethrowers, destructible environments, slow motion and the ability to steer a missile that hit you into the person who shot it. great with friends.