Oh I figured this out a while back.
Wear the Nike/Adidas/fila/underarmor...etc... active wear athletic shirts that aren't compression shirts.
Athletic shirts that are made to evaporate sweat away and all that are made of polyester and such and will fit a big frame without looking ridiculous or being tailored to your exact measurements. They aren't ridiculously tight shirts that hug your shit or anything so you don't look like a huge douche bag wearing them just around in public.
They do breath quite well, since they are for sports, which is a big concern for me as I run hot...And they are cut CORRECTLY to accommodate broad shoulders without being like a dress at the bottom, and best of all they can stretch in the right areas so they don't squeeze the fuck out of your back or chafe under your arms.
Most T shirts I have found that will fit my shoulders/back don't fit right elsewhere because they are made for some fat fuck, I wear a XXL or a XL but I have a 34 inch waist...and Im not 6'5...
For just general, casual, everyday wear... Academy and Kohls are a God send for lifters.