OK, you've found the right bike at a good shop. Having the right accessories can make getting into the sport that much more pleasant. Get a good one and wear it. It is very important to stay well-hydrated when riding, especially for older riders or riding in hot areas. Unless you ride on carpet, you will eventually get a flat tired.
Inflation is a good thing.
Generally, frame pumps are not able to stand up to everyday use, so you should get one of each, and check your tire pressure at least once a week. Some basic tools. It's not difficult to do basic adjustments and maintenance, and it can save you some money. One of those little kits that looks like a Swiss Army knife is a good bet. Also, a set of tire levers will make tire removal and tube replacement easier - get ones made from plastic or nylon.