Most women wear one-pieces in indoor swimming pools, and some wear bikinis for sunbathing by outdoor pools or on the beach. But there's no reason why you shouldn't wear a bikini in a swimming pool, or a one-piece on the beach - it really doesn't matter.
If you in a chlorinated pool and doing a stroke which means that your face in the water a lot, you may want to wear goggles, but you don't often see people wearing swimming caps these days. But you could wear one if you want.
Don't worry about it - there are no rules, and nobody will mind what you wear.