question, when you guys are saying dress shirts do you mean a proper dress shirt (one you would wear with a tux) or do you just mean a shirt that is vaguely formal?
Reason I ask is that someone mentioned button downs. And to me a shirt with a button down collar is a casual shirt (should also never be worn with a tie as it looks awful.)
Not trying to be a dick, just trying to get the lingo straight.
As for European cut, yes expensive designers tend to use the tailored cut but for the most part cheapish shirts will be a similar box shape as the ones you get in the states.
best advice is go to Thailand on holiday. Not only because it is an amazing holday but also because you will be able to get a couple of suits and a load of shirts made to measure for a very small amount of money. Many of these places will keep your stats on file and then you can order more from them over the phone!