Parkour parks are public areas designed for the training of Parkour by everyone, therefore the first thing to note might be that you will be sharing this spot with others. This is a lot easier if you break the ice and talk to them at least to negotiate which direction/area you want to move in to save any unwanted accidents.
There is a lot to offer in the way of sporting footwear and many brands built on running shoes make for great Freerunning shoes with some brand's actually having specific Parkour shoes designed for the activity in question. Some big Parkour brands such as Storror, Jiyo, Ollo, Know Obstacles and Tempest have designed and branded shoes of their own, for the community from the community.
When approaching training outside for the first time students can be worried about the possibility of injury or something going wrong. Rightfully so, considering they are surrounded by hard surfaces and substantial heights it is perfectly reasonable that they approach with caution and attention to their movement and the environment around them.