We have all our insurance covered through Nationwide. When we rented, and there was a little, tiny incident involving kids, fire, and a very old apartment building not up to code, they paid up promptly and without arguing. They've also been good about paying for car accidents (none our fault) and random other car claims, so we figure they're worth it.

I'd also recommend getting more renters' insurance than you think you need. Even with your careful habits about buying stuff, replacement costs for random household goods are surprisingly high, especially if you have to buy them in a great hurry. Which is generally the case if you've had an insurer pay.