Insurance companies make a great play about selling you all kinds of insurance for all kinds of mishaps.
The short version of my advice here is: Don’t, except for liability. The longer version:
If you are the kind of person that wants to have certainty about everything in life then probably freelancing is not for you. It is not without risk and some of those risks are so expensive to insure against that if you did it you’d effectively be working for the insurance companies. I’m thinking along the lines of loss of income insurance and all kinds of other things that have a fairly small chance of happening, cost lots to insure because you’ll be paid out over your lifetime.
The need for any of these varies from location to location, in general if it is something that you have never seen anybody around you put a claim out on you can probably do without it.
Better to take some risk and save. That way if something unforeseen happens you should be able to solve it ‘out of pocket’. Besides that insurance companies have a bit of a habit of trying to weasel out of their obligations once they should pay out.
The only insurances that I think make sense are a good health insurance, and if you are working with customer property a good liability insurance (those are both probably a good idea even if you are not freelancing).
(if you’re in the US have a look here: for some pointers).
Everything else should be considered a luxury, especially in the early days.
Forget about insuring ‘loss of income’ and other such things, the statistical chance of you needing it is small and the conditions required to prove loss of income are very hard to meet anyway.
Of course this says nothing about property insurance, vehicle insurance and so on, those are outside the scope of this book, and usually required by law (depending on your locality).