But we could get some insurance to cover it.

When property was purchases Insurance was not purchased.

Hold in our own name and purchase liability insurance (incl. umbrella insurance)2. 

Do you think it's better to do a FHA on a true duplex and take the increase with the mortgage insurance or to do a cheaper single family where I could create a basement apartment as a makeshift duplex paying the 20% to keep the mortgage low and easier to cover with the rent it would generate?

They ruin roofs left and right and your insurance is higher.You can use a turnkey provider or find a local agent/ pm and go that route if you go out of state.I have done both and think a combination is ideal.

Find a team: lender, RE agent (preferably one who also invests and knows the ins and outs of your strategy), attorney (investor friendly), insurance agent5.

FL in general gets hard because of high property taxes and insurance, and then in the more popular cities like Tampa, general price hikes. 

Is any body using CSE insurance Group?

At a minimum you'll want to make sure the title is clear, and if someone is willing to offer title insurance, all the better.

Medicare doesn't have much coverage at all for this sort of thing.