Honestly, the first movie is actually insane - aside from a 5 second sequence at the beginning, you could watch the entire first Predator movie and be like "wait, was that an alien?? From outer space??" It's very much supposed to be "slasher movie monster, but the monster is actually real / alien"
I love it very much. I went to a showing with a Q&A from John McTiernan a few years back and it was absolutely fascinating. The ending of Predator 2 was originally the end of 1, but they ran out of time with Arnie so had to cobble together something quicker to film (the now iconic self destruct).
I've seen most of the movies - all but "The Predator", I believe. Even "Predators" is not bad. They reversed it, with the humans being TAKEN to a safari planet, while still maintaining the correct horror elements and mystery (like, they didn't explain the other entity killed early on).
But the most recent Predator movie, with Amber Midthunder, felt like a solid return to the core Predator story, while modernizing some of the aesthetic and prop work and tech used. And the fights were appropriately gory and terrifying.
The newer anime is good. Same director as Prey and the next live action Predator film coming is part of the same arc (same director again).