Answer:
A rider wears a helmet for the head
A t-shirt a cotton t-shirt is really good as it allows you to move and it breathes too
Jodhpurs or if you don't have jodhpurs jeans will do and if you don't have jeans just pants NO SHORTS alot of people say wearing shorts while riding is not good for you as you will rub against the horses belly (and you could get itchy legs too)
And boots if you don't have boots in-closed shoes or runners NO SANDALS AND THONGS ECT as a horse ways enough to squash your foot
And for horses it depends because different horses need different things but to ride a horse you need tack (bridle and saddle) and remember stirrups and stirrup leathers too