Release Order:

Alien (1979)
Aliens (1986)
Predator (1987)
Predator 2 (1990)
Alien 3 (1992)
Alien resurrection (1997)
AvP (2004)
AvP requiem (2006)
Predators (2010)
Prometheus (2012)
Alien Covenant (2017)
The Predator (2018)

Chronological (in-universe) Order:

Predator (set in '87)
Predator 2 (set in '97)
AvP (set in '04)
AvP Requiem (set in '04, directly after AvP)
Predators (set in 2010)
Prometheus (set in 2093)
Alien Covenant (set in 2104)
Alien (set in 2122)
(optional: play Alien Isolation, set in 2137 and follows Ripley's daughter)
Aliens (set in 2179)
Alien 3 (set in 2179)
Alien resurrection (set in 2379)


I think both of these orders leave a lot to be desired. So I thought of a more fun "greatest hits" order. While the chronological narrative gets shuffled, I think it's a more fun tonal narrative


Prometheus
Alien
Aliens
Predator
Predator 2
Alien 3
Predators
Alien Resurrection

This omits the less stellar ones such as the AVP crossovers. It begins with a prequel, however I think Prometheus does a generally good job of establishing the "feel" of the universe and watching it first doesn't really spoil much to come. Following Aliens with the first two Predator films establishes a nice tonal arc, since those 2 are similar to the heavy action tone of Aliens. Then you get the proper wrap up to Ripley's arc in Alien 3, followed by Predators and resurrection as fun bonuses. I struggled with whether to include Alien Covenant, as I don't really think it adds much to the lore beyond expanding David's character. If you must include it, then I would do so either between Prometheus and Alien (the chronological fit), or shuffle it closer to the end, perhaps after Predators. One could also just do a "Ridley Scott trilogy" featuring Prometheus, Alien Covenant and Alien, and leave out the rest. Or they could do a more action oriented marathon starting with Aliens, leading into the first 2 Predators, and wrapping up with Resurrection.