I don't have an eternity ring, but I've always believed that the eternity goes nearest your hand, then the wedding ring, with the engagement ring on top - in the order that they were given.
My rings are all gold - eternity first, then engagement and then wedding ring (my wedding ring seems to be the smallest so stops the other two from slipping about (as they seem a bit big)).
Mine are both gold and have wedding first with engagement after. Partly because I hope to never take my wedding ring off but the engagement needs to come off for cleaning.
This is the order I wore them in my previous marriages too :-))
Mine are all 18 ct. white gold. Wedding, eternity, engagement. Don't often wear the three together, only when I go on holiday or out for a night on the town. Don't like to leave them at home in case of a burglary!
Wedding ring first and nearest the heart then engagement ring. No other rings ever on third finger left hand. I didn't used to wear my rings at work as hand hygiene was vital, wearing a plain wedding ring was allowed but it got gunked up with the alcohol gel so I didn't. I no longer wear any rings because my joints swell. Both of my original rings were yellow gold but for our 10th anniversary DH gave me a square emerald with flanking diamonds in white gold.