What I have learnt is that most people wear too big a band size and too small a cup size. If you measure 28.5" under your bust, at least TRY bras with very large cup sizes and 28" or 30" band size. If you have been thinking your band size should be 34" or something, you will no doubt baulk at this idea, as I myself did, but to my very great surprise, it is indeed the case that the small band bigger cup size feels much much more comfortable, and even more surprising to me, the smaller band size made the back/underarm fat problem I had had with the 34D size go away. This sounds patently ridiculous, I know, or at least it did to me before I tried the small band size, but what I discovered is that the correct band size stays completely horizontal as opposed to riding up a bit at the back, and that it is the riding up that is the main cause of the back or side fat problem. Not that you are asking about that, of course. It is just such a common concern, including for thin women like me, that I thought I'd mention it.
Until I compared the two sizes back to back, as it were, I have not even realised that the larger band width size was riding up. It was not dramatically riding up so I had assumed that it was as it should be, and indeed, the M&S bra fitter had told me 34D was correct for me. But I now know that it really wasn't correct at all.
I think part of the problem is that when faced with significant back fat (like on me despite my general thinness) bra fitters think that it is necessary to increase the band size to get rid of the back fat. What that does is to put all the strain of support on the shoulders instead of the band doing some of the work to keep things in place. Fat is squishy so if, like me, you have back fat, you have to slightly DECREASE the band size, if anything, not increase it. I am still not wearing a band size 28, which is what I measure around my underbust, but only because I have not yet found any 28 band size bras. I can definitely tell from the 30 inch band size compared to the 32 and 34-inch band size bras that that is what would work best.
I am not exactly sure what cup size you would be but my wild guess would be in the region of a G cup if you were trying a 28 or 30-inch band size. As with clothing more generally, there will be differences between different manufacturers' sizes, unfortunately. There are specialist bra shops online that offer free returns should you want to order several sizes to find the one that works best for you.
Best of luck!
Sarah