Always wear a helmet while riding. It will not improve your cycling skills or make you a better cyclist but it will protect your head in the event of an accident & you hit your head.

As far as pedals, that is more of a personal & comfort choice. I may want to start out with platform pedals with to straps & either regular cross trainers or even mtn bike style cycling shoes, just leave the rubber cover in place where you put the cleat. After you get used to them or see if you will like them then you may want to add clipless pedals. There is a style Shimano makes that is clipless on one side & platform on the other. They are not very expensive. If you go with bike shoes try on several differant pair & try both shoes on with the socks you will be wearing when you ride. Differant brands & styles of shoes will fit your feet a lot more differant then regular running or cross trainers.

Most bike shops will give a discount on accessories with the purchase of a new bike. Like helmets, shoes, clipless pedals, gloves, water bottles, cages, etc.