A pair of well fitted running shoes will protect your feet from running surfaces, provide traction and absorb shock as you land on your feet. Therefore running shoes becomes the most important accessory in a runners gym bag.
It is highly recommended that you get your foot topographic done from a store that specializes in running equipment. They typically make you run on an a treadmill, take videos of your gait and provide personalized recommendations based on your individual profile. Look for a nearest store at www.roadrunnersports.com or any store that specializes in running gears.
If budget allows get two pairs one for running during the week and another for weekend long runs as it improves the life span of the shoes. Do not use these shoes for any other activity (including walking). It is also recommended that shoes are replaced after 350-500 miles of running as the cushion and sole begin to wear down and reduces the performance and traction of the shoes.
Some of the top running shoes brands:
Do not forget Running Socks($30-$50/3 pairs) and Customised InSole($85-$100) for your feet. Its a great investment to keep feet tightly hugged to shoes. Slips causes blisters which is not good.
Pro tip: You can add running shoes to your running app (Garmin, Apple etc) so you can keep track of the mileage.