I'm not a big jewelry person at all, but for the past 40 years I've worn my wedding ring on my left hand, and an old engagement ring that used to be my grandmother's on my right. It wasn't even the engagement ring she got from my grandfather--she had been engaged to someone and they broke it off and she kept the ring. It's pretty, and that's the only reason I wear it. I don't have an engagement ring of my own. My DH had given me a set of diamond earrings as an engagement gift instead of a ring, and unfortunately they were stolen from a jewelry store when they were there for a cleaning (only time I ever had jewelry cleaned in my entire life--should have probably sued the jewelry store for the price of the earrings, but I didn't).
Fortunately I only have one daughter, and she may want those rings. As far as the other stuff, I don't know. I think it's a good idea to have my kids stake their claim on my stuff before I die.