I get a lot of questions about proper footwear, so I've put together a very basic guide to buying athletic shoes and more specifically running shoes.
Obviously, you want to buy shoes shoes that are specific to the activity you're buying them for. Running shoes are pretty versatile and can be used for a number of activities other than running. Cross-trainers are made specifically for a variety of activities and might be a better choice for an eclectic lifestyle. So if you're doing a wide variety of things, including a lot of running, buy running shoes. If you're doing a wide variety of things without so much running then buy cross-trainers. Other than that buy for you're specific activity.
Athletic shoes, especially running shoes will run a little smaller than casual shoes, so expect to go up a half to a full size. Your foot should not spill outside of the soles; they make wide sizes for a reason. When standing, there should be a thumb's width between your toes and the end of the shoe. This gives space for your foot to expand on impact.
Running shoes are made for specific gaits. Neutral shoes are generally very cushioned and made for those with normal to high arches and a neutral gait. Stability shoes are stiffer, and have medial support in the form of thick reinforced rubber (visible in the photo as grey-webbed rubber between the heel and the forefoot). These shoes are made for folks with mild pronation and a low or non-existent arch. Motion-control shoes are even stiffer, have a much bigger medial post, and are made for heavy pronators that typically have flatter feet. You can also find a huge variety of minimalist and 0 drop shoes for those that wish to closely simulate barefoot running.
Most running shops can help you figure out which style suits your gait and foot. Other than that trial and error will help you determine style is truly the best for you.
It's best to try on a pair of shoes before you buy them for the first time. Once, you know what shoe models work best for you, then you can find great deals on-line. Sometimes prices will be greatly reduced for minor defects or simply because a newer model is available. Specialty running shops are a great place to find shoes for the first time. They usually have a good selection, and a knowledgeable staff than can help you find what you need. These shops get a bad rap for being expensive, but that is because they usually carry higher-end models. Retail prices are going to be nearly identical everywhere, so if price is a big issue, then find the sales.
Some folks are ferociously brand loyal, but the fact is every shoe company makes shoes of varying quality. Again price is a decent clue. It is likely that several different companies make a shoe that you would love. Keep an open mind when shoe shopping.
Replace your shoes often. Your shoes should protect your feet and body from wear and tear. Once your shoes are visibly worn or your body starts feeling more of the bumps in training, it's time to replace those things. Don't be cheap, your body is worth the investment. You can expect to get 300-450 miles of running out of most shoes you'll find at the running specialty store.