Regardless of the brewing method, it all starts with the beans. Since coffee beans are mostly non-soluble in water (approximately 28% water-soluble), the beans must be ground in order to maximize surface area and flow rate to allow for optimum extraction. Although a blade grinder will certainly do the job, a burr grinder will produce a more consistent particle size which will result in a more uniform extraction and a taste that is noticeably superior.
Asking "What is the best way to brew coffee?" is a difficult question to answer. It depends on your budget, how much/little effort you want to put into brewing coffee, and how much control you want over the variables that influence the quality. Drip and filtration devices such as an automatic coffee maker, percolator, and My K-cups® have relatively fewer variables to control which makes it quick and easy for coffee preparation and minimal cleanup afterwards. Pressure/steeping devices such as Aeropress® and the French press are great for traveling and also require minimal practice to brew to your liking. Pour-over methods such as Chemex®, Kalita Wave®, and a myriad of other similar devices allow you to control all of the variables and with a little practice, will allow you to tailor your coffee exactly to your preferences. Vacuum pots are fun to experiment with and look very impressive however are more time-consuming to prepare and clean and might not be suitable for those with an on-the-go lifestyle.