Puerto Rico is an insurance hub and there are a lot of decent insurance agencies available. Homeowners or renters insurance is available and I would recommend it the same as you would get anywhere. I found these to be reasonably priced and they included hurricane and earthquake. Auto is similar, though I haven't had direct experience with it.
Medical insurance, like medical care in PR, is more complicated. If you are on your company's US plan, make sure that there are sufficient "in network" providers in PR to go to. Aetna is the only one I am aware of which has good coverage here. If you are insuring directly here, health insurance is available and is not terribly expensive but look closely. Check if it covers care back on the mainland if you need to go there.