Liability Insurance Supplement would cover any liability you might have to the rental company if you got into an accident, etc...
Loss Damage Waiver covers any sort of nicks and dings and bangs you might incur that they might want to charge you with...
Personal Accident Insurance covers you individually if you got into an accident...
Personal Effects Coverage would cover your personal items if the car got stolen or broken into...
I would check out what your travel insurance might cover to figure out what you might need. I tend to be a wimp and accept all the insurance because it is a bit of a confusing mess, plus I have a hard time saying no to anyone. That is why doing the work thing and having the coverage through that, is so much easier.