If you want to do business before the LLC, you can go ahead. Then, once the LLC is formalized, transfer any assets you've created or acquired to it. For example:
http://www.newyorksmallbusinesslaw.com/new_york_small_busine...
As far as making mistakes goes, the paperwork is simpler than filling out doctor's paperwork on a new office visit. For any gaps, it's not hard to read NOLO, and the experience will help you grow as a business person as you learn self-reliance
And, FWIW, Legal zoom has to push the paperwork through the exact same process. The processing time will be the same either way, but you'll likely pay legalzoom a premium on top of the expedited service fee the state charges them.
https://www.legalzoom.com/assets/modals/modal-priority-rush-...