Get fitted? I have never heard such a thing. Is you son just looking to start running to increase his endurance, or is he looking to run marathons?
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If you exercise regularly, you should be replacing your shoes every 3 months, so keep that in mind when it comes to cost.
Get fitted. No doubt about it. Find a local running store, and have them fit your son. If he has an existing pair of sneakers he has used, bring those in as the wear pattern can help to tell them alot in addition to watching him run. Most stores will have a treadmill in store he will use, or will tell him to run up and down the street outside the store.
Be wary of shopping by cost. First time I was fitted, they didn't even tell me the price until I said which I liked the best. Shopping for the cheapest can end up causing serious discomfort while running, and possible injury. If you tell the store you are looking for something affordable, they should definitely be able to gear their choices towards that direction. But expect to pay 80-100 for them. They can run up to about 160.
If you do go to a local store, buy the first pair there. They took the time to fit you and help you to make an educated choice. If you just try them on, and then buy em online you are hurting a local business that tried to help you out. After you find a style you like, then by all means look online and find them cheaper to buy a second/third pair to hold on to for later. I actually usually luck out and find my shoes at Bobs Stores when they changing models, and get them at a great deal so I use the same "model year" sneaker for a while. And once they no longer have that same "model year", get fitted again. The shoes change from year to year, so even though it may have the same name, it won't necessarily be the same show. Just like a car, a 2011 Ford Focus isn't going to be identical to a 2012 Ford Focus. The shoe company could change their last, use a different amount of cushion underfoot, all sorts of things that can make a serious difference.
The 3 months replacement thing - not hard and set. They should be replaced when they don't feel comfortable, or are showing serious wear. I've got about 6 months on my current pair, which includes 2 1/2 marathons, and 1 full marathon, and I am just getting to the point where they need to be replaced.
Looking at reviews from running magazines, asking for opinions can help you to weed out shoes that just don't cut it, but unless you know your needs they cannot be the only deciding factor. Does your son overpronate, underpronate? Have a flat arch, high arch? Certain shoes are meant to address certain issues.