Generally most shirts are cut in what is called classic style. This has a larger arm hole, and is more generous in the waist cut. For most people this is what they need.
Then you have fitted and slim cuts. Both of these have higher arm holes and less material around the waist. Slim is the narrowest. Fitted is what you're looking for.
You can have a classic style shirt tailored easily, but expect to pay about 10 bucks per shirt.
Pennys has a decent shirt in their Stafford line, and they do have athletic cut. These are generally a cotton poly blend, but they also have their executive line that is 100% cotton.
JCPenney : men : dress shirts + ties
I never buy clothes unless they are on sale, so I am always looking for a bargain. I have a few stores near me that I hit frequently, Kohls, Ross, and Pennys. I also get emails from.
JoS. A. Bank Clothiers - Men's Clothing - Find Tailored Men's Suits & Menswear at JoS. A. Bank
They have great sales with prices slashed regularly.
Ebay is another source that I have used.
dress shirts | eBay