Anime is really difficult to get into if you don't know where to start! Hopefully your friends can kick you some good recommendations! Thanks for posting a little bit about what you like, too. Sometimes it's hard to rec stuff because there's just... so much.
Newer Animes
The first thing that comes to mind when you say action is "Boku no Hero Academia." It's really big right now, and is very popular - it centers around kids with superpowers who go to superhero school and fight evil. It has... several seasons? But not a crazy amount of episodes.
Something that's also "action" but less shounen is "SK8 the Infinity." It's got its drama moments and its happy moments, but the actual skateboarding matches are very action-packed.
"ODDTAXI" - anthro animals! Driving taxis! And lots of twists and turns.
"Tokyo Ghoul" - protagonist deals with cannibalistic ghouls in many ways.
"PSYCHO-PASS" - cyberpunk psychological thriller!!
"Another" - probably for intermediate viewers, but I'm putting it here because you mentioned you like horror. It's basically "Final Destination: The Anime." Lol
Classic, "Everyone knows 'em" Animes
"Samurai Champloo" is also a good action anime that has a couple of subtle adult nods. It's set in historical Japan but has loads of action sequences and a kickass soundtrack.
"Cowboy Bebop" is a classic, of course - a noir action anime that is pretty adult but only really in its themes. Also with a kickass soundtrack.
"Fullmetal Alchemist: Brotherhood." Action-packed anime with drama, horror, and demons. You can't go wrong!
"Death Note" - this is going to hit your paranormal / demon request. A regular guy finds a notebook that kills anyone whose name he writes in it.
"Yu Yu Hakusho." It's best if I sum it up from a copy/paste: "Would you become a detective for ghostly affairs in exchange for resurrection? Yusuke Urameshi finds himself in such a situation after being struck by a car. His innate fighting spirit and street smarts are recognized by the son of the Afterlife’s ruler, and the rest is history." Later in the series it becomes kind of tournament-y, though.