Most definitely a running shop. The choice of shoes is vast and which one is best is based on your own biomechanics. Only a qualified person will be able to tell you what kind you need.

Personally I use a Mizunos 'neutral' shoe now. They tend to be lighter as they use a lot of mesh in their construction.

I've also used Sauchony Stabil, Asics Nimbus, Brooks Beast with varying degrees of success (I have biomechanically odd feet).

Runners world is a good website for a rough idea of what you need and it explains all the jargon that you will need. They also publish all their 'roadtests' as a pamplet every couple of months.

PS Be Prepared to change your shoes about every 400 miles.