I'm an ECE consultant and trainer not a lawyer, so take this advice with that in mind.
Having a small business depending on the skills of your accountant can be very useful. You can write off lots of things. You can also do this with a nonprofit, but you know nonprofits need a board and lots of paperwork, and grants? Those are really hard to obtain. You would think that helping children in need would open you up to all this funding, it was such a nightmare (at least for me)....well the bigger grants that help you do things are going to go the established nonprofits with track records. As a new nonprofit the most you're going to get is maybe $5000, if you're lucky and since you're a new kid on the block they are going to want to see lots of benchmarks reached.
I have run nonprofits and LLC and unless you have a team, the LLC in my opinion is easier for an independent, solo operator. Nonprofits really work best in a kind of cooperative type scenario. You're a preschool, your friends runs a counseling center, another friend runs an afterschool program, another friend runs a clothing store for kids, and another friend has a little league team now that together with an objective is a nonprofit with a ready made board and support to actually accomplish something and put you in the running for grants that can actually do something.
Nonprofits are a team sport.
But keep in mind this is my perspective, scenarios can vary from state to state. If I were you I would join every professional organization that I could, go to a few meetings, get people to know you, and from their you'll be able to figure out the best plan of action.
Legalzoom and a couple of hundred dollars and you have a nonprofit, but I don't think that's the nonprofit that you want.
I hope this is somewhat helpful.
In addition there are probably programs that your childcare center in its current state can be a part of. I know in NJ, NY, and California that if you're in certain locations if you're a childcare center regardless of if it is for profit or nonprofit the state will support the cost for some children. I don't know if there is a state or county childcare/ early childhood agency in you area, but I would suggest you reach out to them or at least find the website and see if there is a reimbursement program in your area and if so how would you go about getting on that list to be an approved vendor of childcare services.