It depends on your state if you'll need a business license. Most states don't require one for the type of work we do but to make sure you should check with your own state government.
I don't have a business license but we are registering as an LLP (similar to an LLC but a partnership instead) Part of our process in doing that is getting a tax ID (although as an LLP we file at the end of the year with our own social security numbers). It hasn't been difficult BUT I did finally just pay
LegalZoom to handle it for me (and am so glad I did

I just don't have time to deal with the forms, etc.)
It was cheaper for me to do it that way, considering the amount of time I needed to handle the paperwork from start to finish - but it's really not that complicated or difficult at all.