Choose a good sports bra. Avoid rough, exposed seams. If you need lots of support, choose a bra with adjustable straps and back. When you raise your arms above your head, the bra should stay put around the rib cage. Choose a bra with low or no cotton content.
Some runners prefer to wear cycling-type shorts that fit tightly to avoid chafing between the legs.
Choose the right type of shoe for your biomechanics. The best shoe is the one that works for you. Don't choose a shoe based solely on how high your arch is. Many people with high arched feet overpronate severely and many people with low arches don't overpronate at all. Be aware that your biomechanics can change over time.