Oh goodie, something I actually know something about!
First, if you do any kind of jogging/running/etc, you are way better off with a running shoe than a walking shoe. Walking shoes don't have the flexibility that you need when you run. When you jog, or run, you want a shoe that is going to curve or bend easily, as when you run and jog, you bend your foot A LOT, and you don't want to have to fight your shoe to do so. Walking shoes should also have a curve, to force you to roll through your foot instead of "slap" but it will be a less flexible and less steep a curve than in a running shoe. BUT, if you play sports, such as tennis, or anything that involves side to side running/moving and not just moving straight forward, you should really consider the cross-trainers. They provide more support for your ankle, so you don't twist it.
That said, there is another factor to consider: over-pronation. If you roll your feet too much to the inside (looks like your ankle or leg is hanging inside compared to your foot) then you need more stability. The crazy thing that happens is that running shoes come in a variety of stabilities. Keeping in mind that, in general, the more stability you have, the less flexibility.
In short, I was told that if you do some walking/some running, you want a running shoe. But if you ONLY walk, you want that walking shoe. Running in a walking shoe is worse for you than walking in a running shoe. And cross-trainers are for sports, like tennis.
Some other things to consider: you should have plenty of room for your toes, but your foot should not slide. You should have about a finger's width from your longest toe to the end of your shoe. The widest part of your foot should fall in the widest part of the shoe.
So, there is no magic brand, just a magic fit. Though, most brands have a certain fit throughout all their styles. (Nike is always too narrow for me.) I worked at Famous Footwear for a while, and I usually recommended New Balance as a start. They are very well-made shoes, with plenty of variety, and are the best brand for having different widths.
Here is one article that deals with such things, however, there are TONS out there. http://www.aapsm.org/runshoe.html