Danny Glover was a name at the time because of Lethal Weapon, so was Bill Paxton, Maria Conchita Alonzo (who also starred in The Running Man) and Ruben Blades, who was also a musician. They also cast Robert Davi, Gary Busey and Adam Baldwin.
The Predator movies always had strong, experienced cast members and people who were household names at the time and had a certain star power.
Casting-wise it all went downhill with the first AvP.