I had that happen to me at my old place. Luckily I was renting a basement apartment in my landlords house, so I just ran upstairs and pounded on the door til they answered (apparently they had a 9:30 bedtime). My landlord and his brother in law are handy and knew what to do. They fixed it themselves the next morning so my bathroom was only out of water for the night (my only hardship was brushing my teeth in the kitchen sink that night and the following morning).
I was very lucky that none of my stuff got ruined or damaged beyond repair, but I was under the impression that if anything had happened, it was up to me and my renter's insurance (which I didn't have at the time... whoops) to replace.
You're perfectly within your right to require your renters to have renters insurance, and what minimums they need to be carrying (my current landlord does at least). As far as what time of insurance you would need, you could always call either your insurance agent or a different company and say you're considering it, what are your costs and liabilities?
Edited to add: Additionally, once you either have a definite renter (or renters) or at least decent candidates, when you're showing them the place make sure you point out "here's the circuit breaker" and all the other important things. iamlindoro is right, I don't think any tenant WANTS to cause damages. That being said, I'm not sure if damages caused by a busted pipe or something like that can be taken from their security deposits.