I'd say there is no single answer to your question. Learning how to best practice Buddhism, in itself is a part of practicing Buddhism. It's not immediately obvious what we should develop, and how we should do this. For example, somebody says we should develop mindfulness, but if we don't have an experience of what being mindful really is like, we won't really understand. We have to develop the experiences that will shape our understanding of what we have to practice.
Also, how we practice most effectively is different for every person. It will depend on our personality and on where we are in the practice. As an example, for some people the precepts became natural and no more effort is required to behave skillfully with respect to them. (The 5 precepts of talking kindly, not hurting living beings, etc.) Then you could say the precepts are not really a practice anymore, can't you? But for others they may still require some more effort, some form of restraint. And this restraint varies from person to person. So the practice is different for everybody.
When we develop more understanding of ourselves, the things we should practice will become more evident. At a certain point we may even get some intuitive understanding how to practice the full eightfold path. But even then how to practice the "best" will be different every day. And at some days you may not even see it as a practice at all because it all becomes so naturally, while at other days you may think you sort of lost it.
Having said all that, I support the replies above. There is some order in how everybody will develop their practice. Starting with moral behavior (the precepts), leading to more awareness which can then lead to understanding. Or as the Buddha put it: Sila, samadhi, panna (virtue, meditation, wisdom)