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.