I have found department stores are great for bras as they tend to have several different brands, and also several fitting rooms rather than having one which is miles away from the actual bra section. So do a first pass where you gather various band sizes and cup sizes relative to your newly measured size. Don't look at colour or style or anything yet, just grab whatever. Go to the fitting room and try them all on backwards. (Cups can be deceiving, or something, I'm not sure how this works, but it does!)
Once you have the band size right, you can try it frontways to check the cups. You'll have to take them off to try them the right way around. You shouldn't be able to scoot the bra around if it fits properly. It shouldn't be moving around on your body, that's how it holds you in place. See what's the smallest you can actually do up, and go for that or one higher, if you're having trouble breathing. You don't want a corset, just a bra! 
Then try anything you have in this band size on the front to check the cup sizes. Do the scoop and fill thing. Four-boob is too small, any space at all is too big.
You might have to do a second pass to grab more band/cup sizes if none of them are quite right. But hopefully at this point, you have a better idea of what fits and what doesn't. Lastly when you've found the right band and cup size, or range, you can look for different styles and colours in this size. It takes a while, pick a time when you're alone and not in a rush, and it might not happen in the first shop you try - as I said, it took me over a year (but I don't go clothes shopping very often.) Also, if you're a "non standard" size shops might not carry the right size for you, which can be frustrating and make it more difficult to try on different bras. But it is nice when it clicks.