The soles of your shoes may be the most important feature. If the soles grip the floor too much, you can strain or twist your ankles, or knees, when trying to do turns or spins. If the soles have no grip, and slide too easily on the floor, you will be constantly fighting the floor on direction changes, slipping enough strain your leg muscles, or even slipping enough to fall.
Regular sneakers or cross-trainers are a bad choice for dancing! The are designed to provide maximum grip, which will eventually lead to a twisted ankle when you dance because the shoe stays anchored to the floor, but your leg and whole body try to turn. For your own safety, wear something other than sneakers.
For most floors, dance sneakers are the best choice. They come in a variety of styles and colors for both men and women and tend to have more cushioning than suede-bottom ballroom dance shoes. They have a special rubber sole that does not leave marks and that allows you to turn and spin almost like suede-bottom shoes. They wear out quickly if worn outside on sidewalks, but they will last a long time if used exclusively indoors
Consider slippery soles for "carpet" dancing. Carpets can actually be great to dance on (they are cushioned) except that regular shoes "stick" to them and women's heels sometimes get "caught" in them. So to dance on carpet get shoes with hard smooth "slippery" soles and wide heels that won't catch. No dance sneakers on carpets, they will only strain your knee & ankle joints.