It's up to you! What's your preference? How experienced are you? What kind of equipment do you have? What do you want to do?
Extract kits are easy, inexpensive and fun! They make great beer, too. Are you a "newbie"? Check out a starter kit at your local homebrew supply store. You'll get everything you need to make 5 gallons of fresh homemade beer. Malted barley concentrate in either syrup or powered form, hop pellets, yeast, fermenters, bottlecaps, the works! You'll probably have to supply your own bottles and cook kettle. A baked emanel 16 qt. pot works great on a stovetop.
Partial mash is basically an extract kit that has a bag of specialty grains that are milled and will be steeped, like tea, in your brewpot before adding the malt extract. The grain adds a dimension to the extract kit by providing a fresh grain flavor and natural coloring, body and flavor.
All-grain brewing requires specialty equipment in order to mash the grain to make wort, such as the "Brew-Magic" Brewing System pictured on the main page of this website. This is a more advanced technique used by experienced brewers requiring additional time and a substantial investment in equipment. More challenging than extract brewing, but more control can be exercised over the process and the results are astonishing!