The question is whether you can do any of that while having boooked through Priceline.

If you're Avis Preferred (free) and book with your Preferred/Wizard number through Avis directly, you can use Select & Go at LAX. But not if you don't have your Preferred linked to your reservation, and I have my doubts that you can link Preferred (even if you do have it) to a Priceline reservation.

With Priceline, you generally give up perks, and get what you paid for, at a low price. If you want "membership" perks, whether with a car rental program or a hotel program, you generally have to book with them directly, not through any third-party booking site.

And you don't get a "selection" at a rental agency where you don't have status/membership. You are assinged a car. Maybe, just maybe, you can bargain for another car, but likely only in the same category, if you're just a "nobody" off the street (which you generally are, with any third-party booking site reservation, whether you otherwise are a member of their program or not).

My experience at LAX are irrelevant. I typically book economy, and drive away in a compact or even intermediate. But that's solely because I am (at least) Avis Prefered, and always make my reservations at avis.com while logged in with my Preferred/Wizard number. So the cars are get are Preferred upgrades (either automatic upgrades they chose for me, or, since the past year or so, through Select & Go), and that's not necessarily at all what someone coming in with a third-party website reservation would get.

By the way, the selections I can make in Select & Go are way better for me than what they upgrade me to. More than half the time at LAX they upgrade me to some SUV, when all I want is a normal car, and so (unless I go to the desk and ask to be "downgraded back") Select & Go gives me my best & fastest choice of cars. (Fortunately, at stations that don't have Select & Go, I don't often get this useless-to-me SUV upgrade.)