Will I run into any major issues if my Driver's License doesn't match my billing address? I moved to a new state recently and haven't had the chance to update my license. Still have the receipt in my email and the form of payment that I used, will that be enough?

There won't be a problem with the difference of billing address and ID. The ID will be used to make sure that you are in fact you, i.e. that the name and face match. They will also ask for the e-mail address associated with your account.