Druidus, I'd say run whenever is most convenient for you. ( Though that is a very interesting piece of information, Bastet, as far as running in the morning goes--never knew that. ) I tend to just run whenever I can fit it in my schedule, and not having a fixed schedule at my job means I may run in the morning, or evening. It also depends on the time of the year, at least if you run outdoors, which I mostly do. In the summer it gets pretty hot and humid where I am, so running in the middle of the day is definitely out of the question. Since the days are longer, I tend to run in the evenings in summer. In winter, with the shorter days, it's more often in the morning.
And as far as shoes go, everyone has different requirements there, but my absolute favorite brand--I wear no other--is Saucony. I have tried others, such as Nike, Asics, etc., and none were as comfortable as Saucony. I highly recommend Saucony's. They make great, high-quality running shoes.