I would say the biggest problems for plums are plum curculio and brown rot… these two problems will ruin 100% of the crop every year once they take hold. If you want to be organic you can spray Surround to deal with the plum curculio, but it takes a lot of practice to get good at that. For brown rot it is very hard to deal with organically and it requires lots of sprays. See my Low-Impact Spray Schedule (2019 Edition) where I list what I did when I was 100% organic. I now use a synthetic for rot control but I still don’t use any broad-spectrum poisons.
Overall you will need half a dozen sprays per year to get a decent plum harvest, mainly spraying Surround for curcs and moths, and sulphur for rot control. Note that these are the exact same problems you will have on peaches. You may have not had your peaches long enough to run into these issues. The moths tend to be worse on peaches but the curc is a bit worse on plums. I need to use spinosad on the peaches for moth control.
In terms of varieties, the #1 issue is brown rot as susceptibility varies. After that fruit set. I would skip Santa Rosa for fruit set reasons but Weeping Santa Rosa and Laroda are very similar in taste but set well. My current overall favorites are Satsuma and Lavinia, they don’t rot much and are very tasty. I don’t like the AUs for flavor, the apricot hybrids are bad for rot, and Chicasaw plums also have the same curculio and rot issues. Skip the Euros for now, they are all super rotters and mega knotters.
Most J plums will pollinate each other as their blooms tend to all be similar enough in timing.