In most companies, one of the prevailing project management methods has been chosen and adapted to the corporate language and culture. If so, there is little choice in the matter for the ecommerce project, deviating will result in a lot of discussion and interpretation. The best way is then to focus on the development method. Understanding the different methods is, however, valuable to see the focus of the existing method. (As it is default and everybody does it this way, these paradigms run deep).
If you have the freedom to choose, take the time to do so. As this will fundamentally set the stage for the project and possibly subsequent projects.
A good and concise overview and history are found on wikipedia. In the Wiki, development methods on agile and project management seem to be combined. For lean and extreme project management there are no existing or emergent standard. The traditional method is simple and concise, but gives little guidance. It helps to have a method to stick to, especially when there is a lot of work and pressure, as focus external stakeholders is the first to be on second plan when there is a lot going on, but is crucial especially then.
PRINCE2 is extremely helpful: It has a framework with waypoints and communication templates. It defines reporting, but does so from a view on outputs and quality, not on acitivities and tasks. This means that reporting is on deliverables and exceptions or issues that arise. Another advantage is the definition of roles: PRINCE2 defines speicifc roles and responsibilities for stakeholders. The phasing can be aligned with Scrum or DSDM: a PRINCE2 stage can be set to a release and the first three phases of DSDM align with Starting Up a project in PRINCE2. Another advantage is that most project organisations and professionals have some understanding of PRINCE2 and its phases.