One of the reasons I love running is that it really requires no special gear. You just need a body and a desire to run. Then again, you might not need a racquet or clubs to go for a good jog, but I would suggest quality running shoes.
If you are taking up running, good quality running shoes can seriously make this habit stick. Old shoes, tennis shoes, cheap shoes often don't provide enough cushion to protect your feet, ankles, and knees which can lead to injuries and prevent you from learning to love running. Since shoes are really the only important gear needed for running, I wouldn't skimp on them. You don't need to pay out the nose for some newfangled shoe, but generally what you pay for is what you get. Expect to pay around $100. Which may sound like a lot, but can you really put a price on your knees? Plus, maybe the guilt of an expensive gear purchase will motivate you to run.
Look for a well cushioned shoe that fits your foot, matches your foot type and gait pattern. The best place to start this endeavor is a running store since they tend to employ people obsessed with running. Therefore they should be able to help you figure out your gait and point you toward the shoe for you. The American Council on Exercise recommends shoes with greater shock absorption for runners with high arches, which may make you more prone to ankle sprains. On the other hand (or foot I could say), if you have low arches look for a shoe with greater support and heel control. Here is a list of running shoes rated by the The American Academy of Podiatric Sports Medicine. It should help you figure out what brands could be good for your needs.
Fit's Tip: Buy a shoe that’s as wide as possible across the forefoot without slipping in the heel.