I'd say that if we're talking Arnold, I have no complaints about Conan the Barbarian getting listed. Conan the Barbarian is probably my favorite film of all time. It casts a long shadow of pop culture, and it was one of the two performances that made Arnold a star. But if we're disqualifying movies with super powers, Conan, containing shapeshifting, hypnotism, resurrection, ghosts/demons, would have to also be disqualified.
Instead, I'd have to go with John Matrix from Commando. It has some of Arnold's best one-liners, has classic action, and is soaked in the 80s. The more flippant attitude is what edges out Ben Richards and The Running Man (though I'd account that one the better movie).
Heck, I'd happily fill a top ten list with at least half of the entries belonging to Schwarzenegger (as an aside, he has a mailing list that goes out once a month that is well worth subscribing to).
Indiana Jones has to be on a top-ten western action heroes list, because he is the two-fisted distillation of so many classic pulp heroes and tropes.
Additionally, I'm going to include the following, which break one or more of the rules:
Ellen Ripley
Coffy
Imperator Furiosa