I watched through the whole Alien series this year, and then circled back and watched all of the Predator movies. I 100% recommend Alien through Alien Resurrection. Prometheus and Covenant: they have extremely fascinating premises but fail to deliver on what could have been really deep themes. As a result they end up just being vehicles for events happening and people dying and it's not that interesting.
For the Predator movies, I would recommend Predator, Predator 2, Alien vs. Predator, and Prey.
Aliens vs. Predator: Requiem was too dark, had a completely different tone than the original, and didn't really do anything to contribute to the world. Predators had a few good action sequences and plot twists to it but overall it was just a really bland idea - random people who you never really care too much about end up on a planet being hunted by Predators and they're just trying to survive. And The Predator was a borderline family drama with generic and awful "commentary" about the military, and way too much terrible comedy to take seriously. It has Keegan-Michael Key in it, I think that probably says enough (I like the guy for the most part but he's a comedian and... he's basically just telling jokes the whole movie.