Most questions can be answered here-
Go to the shoe store and find a pair of shoes that feel comfortable. They should be running or cross-training shoes. Skate shoes, casual shoes, walking shoes, tennis shoes, etc. are almost always not what you want because they don't allow for athletic movements or proper running. The shoes should be light, breathable, flexible and have softer rubber on the sole. The sole should not have any plastic whatsoever. Fancy "shox" and nonsense on the heel should be avoided. For this reason, many traceurs prefer the cheaper range of shoes as they are simpler. Padding or shock absorption should NOT be a consideration. All shoes provide plenty and it is up to you to train and be the mechanism that absorbs the shock. Some practitioners like to wear ultra-light weight kung-fu shoes. These provide almost no padding which forces the wearer to have good form and technique. They are also very flexible which allows for a better feel of the ground and other surfaces. Parkour-specific shoes are a decent choice but can often be expensive and hard to obtain. These offerings also often sacrifice certain features such as response and proper running support.
Beyond this DO A SEARCH for specific shoes and questions!!