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!
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.