Each person has a different concept of what the perfect shoe should look like. All features are important, but what is most important is what you most like. If you get a shoe based only on what someone recommends, you might not like the style or fit, and will not like the shoe. It will not be the best one in your eyes.
In addition to style options, structural options need to be considered. Styles change often, but structural qualities not so often. Styles change as preferences change, but structural features only change as new information is discovered about what the foot needs.
Style helps a person make a statement with their shoes. Though fit and function have to be accommodated, there is a lot of latitude in selecting style. Color is one thing that can be selected according to preference. There are all sorts of colors, from the neutral black, white, and gray to the whole range of the spectrum, including red, green, purple, orange, yellow, and others. These colors can be combined in any number of combinations. You should be able to get any color or color combination that you would like.
Another aspect of style is uppers. They can be low-top, mid-top, and high-top. Some, called boots, even reach to just below the knees. They can be made from a number of materials. You can get them in vinyl, leather, canvas, and a combination of any of these. Different design features are available, such as brand logos, team logos, and just abstract designs. These can be in contrasting colors, or tone-on-tone.
Most all shoes have their brand-specific design element, such as a logo or other identifiable design. The names usually indicate the feature that they company wants to portray, such as shoes with air in the soles, called something air, the something being the name they want to use.
Claims to help you jump higher or run faster, shoot more baskets, or other such claim to fame is not really a style element, but rather a sales technique. Yes, since they allow you to make a particular statement though the shoe you choose, they are still somewhat of a style element.
Soles may not be a major style element, but they are still very important. They do come in a variety of colors, and have designs in them. But, their most important aspect is that of fit and flexibility. That is what makes them better than an ordinary shoe for athletic uses. The latest trainers have all the aspects of functionality, but with a variety of style elements that can please even the most discriminating persons.