Welcome, Aiden's Mommy! At one point in my life, I also looked into opening a boutique of this kind.
For one thing, you need to contact your bank and find out if they think your business is a good prospect for a loan. If they refuse you, you can always try the back door approach (get a home equity loan, or max out some credit cards).
It's easy to get a business license-- you may want to contact your local Chamber of Commerce to find out the address in your state you need and to help you fill out appropriate forms. City hall can also help you with this. But it is a really simple process.
Your costs are likely to be these: 1) rent 2) electricity and water 3) childcare 4) merchandise 5) Internet and computer 6) cash register 7) being able to accept credit cards 8) display options for your merchandise (shelves, racks for puzzles and books, hangers for clothes).
You also need to start looking at the labels of products like the ones you want to sell and start contacting manufacturers and finding out what their minimum orders would be, what amounts, what prices. You can then figure out your budget: I want to have ten puzzles, fifteen onesies, and twenty of these great rattles.
The key, I think, is to make sure you have enough merchandise in the store to look well-stocked, successful, and interesting. You want people to come back. You could also think of events you could have: reading books to young children once a week; a playroom for young children while their mothers shop; delivering products to a baby shower; gift wrap; seasonal events. "Events" will draw customers into your store.
I hope this helps!