If you have high or low arches, make sure the shoes support your arches properly.
Some people get custom orthotic inserts to assure proper support.
Shoes should absorb shock as you land. Shoes that are too firm will feel like you are running on bricks. Shoes that are too soft can cause your feet to be unstable and the shock can go right through the soft mid-sole to your feet. If the shoe feels strange or alien on your feet, forget it. Good shoes feel right when you put them on.