It depends on what type of dancing you're doing, but I'd always recommend you use the correct footwear that corresponds with the type of dancing that you are participating in. For example, ballet shoes are flat, soft shoes, whilst ballroom dancing shoes are small heeled glittery shoes and tap dancing shoes already have 'toes and taps' underneath them.
In general though, you have to wear something that is comfortable as you'd be on your feet a long time, and I'd always say if you can choose between high heeled and a slightly flatter shoe, choose the flatter one, especially whilst learning, as your less likely to take a tumble or fall on a well balanced shoe.
The Right Dancing Shoes
Dancing Related Information
Finding a good pair of dancing shoes may seem like a challenge, but just know they are out there waiting for you. First and foremost you need to decide which dancing shoes are right for you. If you are a dancer of a certain modality then you should know which shoe is appropriate for the job. For instance you would not get Pointe shoes if you are a tap dancer or vice versa. Make sure you know what you're looking for, and you have the best chance of finding it!
Source: Recreation-and-Sports:Dancing