Isn't FlyWithKaeMarie after a different answer: the three airlines you mention are all in the same OneWorld Alliance. You should choose just one FF programme from one of these airlines and use that FF membership to accrue mileage and tier points when you fly on all these airlines into that single FF programme. This is how you move up the tiers and get more benefits/privileges.

If you open accounts and save points in the FF programme of each individual airline then it's unlikely you'll accrue enough miles and tier points to be useful for redemptions/upgrades/lounge access etc. Unless you're a road warrior and flying in business class with all these airlines all the time which is unlikely given the question you ask.

Generally people choose the airline they fly the most with. Choose one and stick with it. When you reach the next tier with that airline the benefits will apply across all OneWorld airlines and you can redeem your miles on all OneWorld airlines (for example, I redeemed Malaysian Enrich points for a Qatar flight - it was fewer points and less cash than redeeming on Malaysian itself).