Neutral shoe = bad for "overpronators". Even if the first time out it feels "more natural", you will break the shoe down unevenly very quickly and will be running on inwardly slanted wedges. Trust me, this is a recipe for disaster (I've done it).
You hear lots of talk here about "strengthening feet by barefoot running" and other reasons not to use the proper type of shoe. I will say that this is not 100% without merit, as there is plenty of truth to the idea that training your foot to strike properly through barefoot running can reduce impact forces. And a little barefoot running can indeed strengthen feet to provide more power during races. But as far as the level of pronation support you need, there is no way to fix this by strengthening. The foot at rest forms an arch, and the reason arches are so great is that they are self supporting. The arch in your foot will actually support your weight without a single muscle firing, so it is this physical structure of bones and ligaments (which cannot be "strengthened" by exercise) that needs support, by the proper shoes or even inserts such as orthotics or over the counter ones like superfeet.
Go to your local running store and get fit by someone who knows feet, shoes and running best. No one can recommend the shoe that will be best for you without you trying them on. You might have to pay retail price instead of $20 off last year's model online (ZoMG!!1!11) but it's worth it.