Jeff -
Your first safety net should be placing your properties into LLCs and/or trusts. I'm not an attorney so I can't give legal advice but every RE attorney I've met says to, at a minimum, place your properties into an LLC.
Your second safety net should be adequate property insurance with liability. This is called the primary insurance and will be the first to pay if an occurrence happens. I would suggest $1M liability per property. Liability insurance is cheap enough it's not worth skimping on. Most policies and most agents will suggest $300k liability coverage but that goes away real fast when a jury is involved.
You umbrella liability policy (personal or commercial) should be your third safety net. Umbrella policies are excess coverage which means they don't kick in until your primary (property) insurance is exhausted. Occasionally a claim can go over even $1M liability so this is when it's good to have the umbrella.
I hope this helps!