Software methodologies are purely a means to reduce project risk.
It's fairly well known that if you take a team of developers practising some methodology and tell them they don't have to follow it anymore and can work however they want, their productivity will increase, but the risk that they will build the wrong thing at the wrong price in the wrong amount of time will greatly increase.
Thus in order to choose an appropriate methodology you first need to determine what the risks are if the project fails.
If the only thing to lose is a couple of weeks of your evenings then a few sketches in a note book and no measurement of progress or deliverables is fine.
If the lives of seven astronauts and billions of dollars is the price of software failure then you better have world class planning, development process, project management and testing in place.