I can only talk about the UK, but there will be crossover. Equipment insurance first off. Public liability second; just in case someone should get injured (or something broken) while you work... and professional indemnity should you fail to provide the services contracted.
Just re-reading what I wrote earlier, I hope it didn't come across harsh or too forward? There are just so many hidden costs involved, that I wish I had known of when starting out and establishing my pricing.