If you have no idea where the likely prospects may be found, do a search of past posts here on SF. Moderately priced dress shirts have been mentioned in a post or two here, over the years.
Me? I like Brooks Brothers. But my fabric and tailoring preferences may not be your preferences. My build may not be anything like your build. My needs may not be anything like your needs.
If there were truly one source of dress shirts in staple colors which was unarguably better than anything else near its price point, that one source would dominate the marketplace and most of the competition would be out of business.