Regular orienteers wear light nylon running clothing, often with a club logo and shoes for running in rough terrain. Any suitable clothing is fine. Rules require full leg cover except when shorts are specifically permitted.
Many people have compasses that you can attach to your thumb with elastic; there is the electronic recording device (SI card (dibber) or (e-tag) which straps to your finger or palm.
It can be compulsory to carry a whistle.
Some use a clear plastic control description holder for the wrist so you can keep it visible and dry easily. This means that the only thing you have to keep a hold of is your map.
None of these gadgets are essential to buy except possibly a compass. If you are taking part in a large number of events it may be worthwhile buying an SI dibber otherwise hire on the day.