Gardens are always part of something else whether it's a small cottage or a rambling mansion. It is this garden setting that helps define the style of garden that would most likely work. More often most people must incorporate the existing landscape or lack thereof into their plans. Community ordinances may prohibit putting a big sprawling vegetable garden in the front yard, they probably also would prohibit putting a large Greek statue out front as well.
Ideally, when planning a new garden or adapting an existing garden, you should consider what you want and how long you expect to remain. Don't try to create a space that will stand forever. Instead consider your needs, wants and desires and work with those. In the end the results will be a blend of those, your budget and your energy levels if you intend to install or maintain the area yourself. When considering these elements, you'll most likely favor one particular garden style over another, and that will depend almost entirely on your personal tastes which can be quite broad. Seldom does one person's likes fit neatly into one particular style.
Like the thousands of plant types that have been classified, gardens types have also been classified. There are broadly 4 different types of gardens with a unlimited amount of type mixing.
The two broad garden types are formal and informal. Everything else is a variation of these two types of gardens that each date back centuries. These types of gardens are considered classical in nature whether they are based on Roman, Greek or Oriental inspirations.
The royal kingdoms are most associated with the formal garden. They had unlimited funds, unlimited man-power and other resources so that even the most laborious landscape could be built and maintained. While the royal kingdoms may be fewer today, that does not mean that we can't incorporate those same principles of symmetry and design into even the smallest setting. You don't have to have acres of land to have a formal garden.
The informal garden could arguably date back to the Garden of Eden with God as the supreme Landscape Architect. The informal garden today is similar: it usually follows fewer rules, was created by perhaps just one person and may or may not be maintained. Informal gardens can attempt to duplicate Mother Nature in a controlled chaos style, or replicate elements of nature in a less random style in that each of the plants were selected and planted in a particular location.
Informal gardens can also have themes whether they be rose gardens, hosta gardens, specific color gardens, or even fairy gardens. By their nature informal gardens have less structure and are more free flowing.
Those are the two broad categories that most gardens will fall under. Under those categories we might find container gardens, rose gardens, small space gardens... the list is almost endless. If you're not sure about your gardening style, check out the library and visit some public gardens, or go on some house and garden tours that are popular in many communities. These will give you some good exposure to a wide variety of garden styles and let you develop of style sense of your own based on what you like.