Many flowering trees and shrubs grow and pretty much take care of themselves. There are thousands of plants cultivated exclusively for their blossoms.
Annuals
Flowers that bloom once a year and die in winter. They are often the most vibrant. Petunias, Impatiens, Snapdragons, Begonias, Vinca, and Pansies are all popular annuals (although pansies survive a mild winter).
Perennials
Perennials typically bloom once or twice a year, die back in winter and shoot back up in spring to bloom again. They have bulbs. Many sport beautiful flowers. Daisies, Black-Eyed Susans, Salvia, Phlox and Clematis are popular perennials.
Again, just a few ideas to get started. Flower gardens greatly benefit from the presence of bees, butterflies and hummingbirds. If you see these creatures around in spring, let them do their thing.