Having a document notarized does NOT give it any legal authority. A notary public will watch someone sign a document, and then ask to see some ID. The NP will then enter the particulars of the ID, the time and date, and notarize the document. A document that's been notarized just means that there was a legal witness to the signing of the document. The document can be complete nonsense, and if it's signed, and the person who signed it produced proper ID, the NP will notarize it.
Having said that, a notarized statement would indicate what your wishes were. But if you didn't word your statement correctly, or if there's some legal basis to overturn the document, it won't hold up in court.
Most lawyers don't charge much for a simple will, and many will even give a discount if a married couple both get their wills drawn up at the same time. It sounds like you don't have much in the way of assets, and your wills would be very simple. If you have a child, you really do need to make wills.