For example...is liability insurance needed? There's currently no office, so it's not like someone can slip and fall on the sidewalk (a commonly cited example for why to get coverage). Also, are there other types of coverage that are particularly relevant for web-based businesses? Thanks!
There are two basic reasons to get business insurance.
First, if you're making enough money that you're worth suing. That does not apply in this case.
Second, if your clients require you to have insurance before accepting you as a vendor for certain services. Most large companies will require service vendors to fulfill certain liability requirements. But for a SaaS offering, especially if the pricing model is a low subscription, you won't trigger the conditions that have their purchasing department demanding you get insurance. It applies more to vendors who are either offering personalized services (like consultants) or service providers who bill very large dollar amounts.
So get insurance when you first start making pots of money OR when a first large enterprise client makes it a condition of working with you. Don't waste money before that.
I applaud your attention to detail but this is a detail (and expense) best reserved until you have an MVP up and running and some evidence of customer demand for your business.
In bootstrapping any business, it's important to minimize your expenses until each expense is justifiable. Business insurance is a great example of an unneeded expense at the pre-launch phase of your business.
None at all.
Because: You're just starting.
You do need to form an LLC or Corp and honor the rules therein such that your personal finances and liability are separated from those of the business. That way if the unthinkable (and very improbable) happens, and the business is sued out of existence, that's the limit of what happens.
Your business is likely to fail for all sorts of reasons. Failing due to an event which would be covered by any of the various forms of business insurance (E&O, liability, etc) is almost certainly NOT the way you will fail. Any second you spend on that is time you should be spending working on not failing in all those other ways.
Once you have something lose, something to protect, then the tables turn and indeed it is reckless to not protect that with insurance of various forms. Also some large customers will require you to carry minimum amounts of various insurance policies.
But that's tomorrow.