You'll have plenty of excuses not to get outside and run during your 10K training program. "My feet hurt," shouldn't be one of them.
Feet are about as different as there are reasons for competing in a race in the first place. To ensure you have the right type of training shoe for your particular foot, first figure out if you're an overpronator (you use the inside of your foot more) or underpronator (you walk on your foot's outside edge) by taking the "wet footprint" test. Simply wet the bottoms of your feet, and then step on a piece of flattened cardboard. If you overpronate, the imprint will be that of a nearly complete foot with your arch coming in contact with the cardboard. If you underpronate, you'll see mostly the toes, heel and outer edge of your foot on the cardboard.
Once you know how your feet contact the ground, you can shop for a shoe that works with your gait, or your pattern of movement. Other things to look for in a good running shoe are that your heel doesn't rub in the back, there's still room in front of your big toe, the shoe is lightweight and breathable, and, most importantly and perhaps obviously, the shoe feels good when you put it on -- no break-in period required.