Not sure about online, but in that price range, I would actually go to H&M. They make surprisingly decent dress shirts and put good attention into the fit. Not sure if you have an H&M near you though. Even the Bay can work pretty good, Ben Sherman or Kenneth Cole slim fits both have a nice cut to them and are affordable, especially with the constant sales at the Bay. Zara is good too and should run you around $60-$70.
Le Chateau and Mexx are garbage, good call there. Stay away from cheep, shiny shirts.
Personally, I'd have to try on a shirt before buying it, or at least know the sizing I like for specific brands and cuts as they will all be the same. No 2 brands are the same, so just knowing your neck size and shoulder width isn't really enough to ensure good online luck.
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