Is a notarized, handwritten will legal?
Yes, it is. A handwritten Will is called a "holographic Will". Some states do not recognize such Wills or only allow for them in limited circumstances. However, AZ recognizes a holographic Will if it is written entirely in the testator's own hand (ie in the handwriting of the person making the Will), and dated and signed by them. No other formalities are required; it does not even have to be notarized.
Depending on the type of estate you have (simple or more complicated), you may still want to consider having an attorney draft one for you. They can best handle all of the complexities involved and you would have the assurance of having your estate distributed according to your wishes and state law. In lieu of that, you could download a form from the Internet (many sites sell such forms), and then make a more formal Will out yourself. Or you could write your holographic Will (or execute one downloaded as described above), then pay for an hour or so of an attorney's time and have them review it for you.