It doesn’t cost the earth to kit yourself out for freerunning.
Freerunners generally wear a light, comfy clothes. The emphasis is on freedom of movement so anything you wear should not impede your ability to complete the various movements you’ll need to do.
Some people wear thin athletic gloves to assist with grip and protect against abrasive surfaces, such as brick and concrete.
One important part of your arsenal should be a good pair of freerunning shoes. Running shoes are good, but rarely offer the grip you’ll need to take on vertical objects or slippy rails.
There are a number of freerunning-specific shoes available if you have a hunt on the web.