There are different kinds of Obstacle Course Races (OCRs). They range between 3 (5k) to 60 miles, contain 15 or more obstacles, and take 30 minutes to 10 hours to complete, depending on your physical conditions. If you race, you know your body will use up everything, leaving you prone to cramping and other assorted race-related issues.
Lightweight merino wool or cotton baselayer. Baselayers are the tops closest to your skin.
Shorts. Wicking. Spandex, cotton are OK great.
OCRs are wet and muddy and regardless of the traction on your sole, you'll never have enough traction. Additionally, that mud never seems to get out, so any sturdy pair of boots, shoes, or sneakers that you were going to throw out anyway is fine.
Backpacks to carry light snacks, something packed with protein and/or energy. (There is always water to drink at intervals throughout the race). Something to help with chaffing (for example, vaseline)
Any and all braces you need
Extra change of clothes (including underwear)
2 large garbage bags
Dry bag and/or ziplocks for your phone, camera, valuables
Please note that you will have to thoroughly rinse everything off after you're done