Defo get her fitted if she will agree My DDs both refused point blank and spent the first few years in the wrong sized bras... It was only when we got to bravissimo only sizes that they agreed to being measured!
Independent lingerie shops are very good..but often don't have much of a range, so might be worth getting measured in one then hit the town for bra shopping?
I second the slightly padded ones being good for nipple hiding. I was horrified when I first saw them,cos you wonder why a child going through puberty needs padding, but actually it does a different job!
Are you absolutely sure she needs one? IMO, they don't need one until they start feeling self-conscious without. If you think she won't like it and none of her friends have one yet, why not let her stay in crop tops a bit longer? If it was me, I'd let her know that you're happy to take her bra shopping whenever she's ready and then wait for her to tell you it's time.
But when it is time, yes - M&S is the best place to go. Don't lay out too much money on posh brands as she's likely to change shape a lot over the next few years.