I dunno, I've never had trouble with "shin splints". I use quotation marks because it's a really broad term that people use for everything that hurts their lower leg.
One of the most important things for running is the shoes. This should be your first port of call, not the last. Your feet are the only place that have contact with the ground and your entire body weight is impacting on it. It's like an F1 car, you can have the best engine (cardio/respiratory system), suspension (joint structure), bodywork (skeletal muscles), fuel mix (food and drink), driver (motivation), but if the tyres (trainers) aren't in good condition and of the right type you are going nowhere.
Get some with solid support/a strong sole (not light), you don't need anything fancy (I've never spent more than £30 on running shoes). Also don't go balls out running straight away, you'll need to wear them in first. I normally just wear a new pair of trainers around the house for a couple of weeks beofr egoing running in them. I know when you run you put different pressures on your feet than when you walk, but you need to get them comfortable to the shape of your foot and make the sole flexible. And try them in the shop, take your time, even if you look like a spazz. You'll look like more of a spazz hobbling around later.
