This is such a good idea.
The question with renter’s insurance you should ask is how much hardship will you suffer for the $20 or less you’ll pay a month? And then ask how much hardship you’ll have if you get burned out, lose everything, and have to try to find some place to sleep at night. (For me, I always phrase that question with the rider, in the middle of a snowstorm in winter - but I don’t know where the OP lives.)
The OP will have to make his own decisions about whether he wants coverage for theft, and at what level. ISTR that some policies have different replacement values for fire vs. theft.
As for not having enough insurance - that can be very, very costly.
MY grandfather owned his own tool & die shop. He used to invite his shop out to his farm for a 4th of July picnic. One year, one of the workers had much too much to drink, and snuck into the barn, and started joyriding on the tractor. It was one of the old, high center of gravity models. And it rolled, killing him.
My grandfather’s initial reaction was to tell the widow that he would make sure she got his pension, and that he would cover the college costs for all the kids, as well. She was inclined to take that offer, until someone hooked her up with an ambulance chasing lawyer. She tried to make a claim for wrongful death, to get even more, and when my grandfather talked to his insurance company - they were of the opinion that since their liability for personal injury was so low, it wasn’t worth it, to them, to fight the claim. They’d pay their share, and just walk.
My grandfather had to hire his own lawyers, and fight it on his own. He did win, but he was hugely bitter when he found out, after the event, that some neglible higher premium would have had the insurance company liable for something like 100 times their share - and his agent had never mentioned that to him.
So my grandfather also changed insuance companies and agents after that.
Don’t just look at the cost of the minimum coverage (IIRC most rental policies are pretty generous for the single person living alone, but take the time to make a real assessment of what replacement costs for you might be. And what your liability coverage should be.) ask what the cost for the next level of coverage might be, as well. It may well be that the OP is best served by the minimum policy, but take the time to make sure of that, before choosing to go with it.