You have DL benefits and if you are LAX based you get American benefits as well. I have no experience with those so can't comment.
Priority is S3C on Delta, ahead of buddy passes but behind retirees/parents. It's not great but it's what every regional goes as, except for Endeavor, they trump us as a wholly owned. First/business class... domestic, it's rare but it happens. Just got it on a pretty empty leg... but usually you're in the back. Internationally, quite possible, I've been in Delta One internationally a lot this year. My mom came as well and also got Delta One both ways... family travels as S4 with today's date as DOE, basically even below buddies so the flights better be wide open and better have a backup plan or zeds. Yield fare for parents. $/fees would be the yield fare for parents and also I think you pay $99 per flight year.