If you wanna ogle monster boys, Megaten, Digimon, and Yokai Watch are some places to go with lots of fanart and whatnot.
Nocturne seems to be the most common entry point into mainline and recently came out with a remaster. There's a bunch of different spinoffs like Digital Devil Saga (more character driven), Devil Summoner, and Devil Survivor (srpg). Strange Journey is a dungeon crawler. The mobile game, Dx2, is actually pretty decent gameplay-wise for gachashit.
Anime-wise, Adventure and Tamers are widely considered the best, Savers if you want more, Appmon is divisive, Xros Wars sucks don't bother. Game-wise, "World" games tend to be monster raising sims and "Story" games are typical JRPGs. Cyber Sleuth is the most recent game and widely available including on Steam. ReArise is a mobile game and decent for what it is. There's also various manga of various quality if you want more out of the franchise.
A lot of people start with the 2nd game and then go into 3. The anime is hilarious and recommended if you want some comedy. Shadowside anime and Forever Friends movie are a more dark take on the franchise, along with the 4th game which unfortunately hasn't been translated yet. The mobile game Puni Puni isn't the best but it's there. There's undubs of the games floating around if you have a hacked 3DS.