I've just finished building my first project (or rather, the first I've brought to completion) and am ready to start finding some early adopters. At what point is it important that I register my business? I haven't yet because I feel like I should validate product/market fit before bothering with the paperwork.
It's just me, no co-founders, so it would be a sole proprietorship.
Check your local laws, but usually before you are legally allow to do any business or transactions you must have a business license.
Since you are a sole proprietor you may or may not need a license depending on what you are selling and where you are selling it.
For example if you are just selling an app in Apple's store you most likely do not need a license. On the other hand if you wish to engage in a profession like law or medicine in the USA you will need a license.
If you live in a state with sales tax, and you are selling taxable products at retail you most likely need to register to collect the tax.