Aren't mods great?
I'd argue that the original Aliens vs Predator is still worth a playthrough, but if you're after an Aliens FPS fix that's more guns blazing, Kontra_Kommando has created a perfect mod for Doom.
Called Aliens 2017, it's a remake of a mod from 1994 for the open-source GZDoom. The download is just under 70mb, and doesn't require any advanced installation beyond just dragging all the files over the GZDoom directory.
I love that you have a limited supply of turrets and other items, which you obviously need to survive. It also looks super effective - this would scare the shit out of me if I played it at night with the lights off.