When you're buying your outdoor patio umbrella, to ensure it doesn't fall over in the wind, you want to make sure it is anchored in some way. An anchoring system or structure that is attached to the bottom and weighted will create a stable umbrella that doesn't blow over in the breeze. You can also buy furniture weights for pretty cheap which will help keep your furniture from blowing away.
Putting your patio umbrella in the center of a table is also a good shout that can balance the structure and make sure it doesn't tip over. Look out for dining tables with holes in the center to support your umbrella.