It's interesting. Take a look at these real world examples of cultural greeting and see what the first ten have in common
1. Shaking hands.
2. Raising a hand as you approach.
3. Kowtow - kneel down and lower your forehead to the ground.
4. Prostrate yourself - lie down on the floor before your superior.
5. Grasping each other's forearms.
6. Bowing to each other - whether low or high, or with a flourish.
7. Saluting your superior.
8. Removing, or simply doffing, your hat.
10. Kneeling before your superior on either one knee or both.
11. Cheek kiss.
12. Cheek pinch.
13. Beating one fish against your chest.
14. Punching your fist in the air.
15. A smile, verbal greeting, and maintained eye contact.
Many of these greetings have one or more of these aspects in common.
1) They involve lowering yourself so that your height is beneath that of your superiors.
2) They involve showing that you're unarmed.
3) They involve putting yourself in a vulnerable position - particularly the kowtow and prostrating oneself.
Each one of these different greeting gestures has their own meanings. A society that prostrates itself before the magistrates will be very different to one that simply doffs its cap or even thumps a fist against its chest. Prostrating oneself is about as humbling a greeting gesture as one can comfortably get whereas doffing your cap (simply tipping the cap back and then settling it back down) is fairly casual and friendly as its a quick and easy gesture. Thumping your fist against your chest is an aggressive act but since it's a greeting and not an insulting gesture it may indicate a remembrance of the power of the law or an indicator of a previous oath sworn to defend the law.
So if you're looking at which sort of greeting your protagonists should use, particularly if they come from an invented society, take a look at that list and see which one they would likely use and why.
If you know of any other greetings that don't fit any of those categories, let me know.