The article said the best way to tell if your clothes are see through is to look at yourself in natural light - sunlight.
Now the bridal salon will probably not let you leave the salon to check and once the dress is yours you don't want to take any chances in getting it dirty or damaged, so rely on your family/friends and the woman fitting you at the salon to tell you if anything is showing. And if the fabric is sheer and you're not sure ask the seamstress about adding a lining or wearing a slip.
If you can't find a good bra to fit talk to the seamstress about sewing cups into the dress, and as for undies you're just going to have to try a few different styles and colors till you find the right one. Going commando is always an option but make sure that truly is the best option before the wedding day. You don't want to make this call on the big day.