If she's only 10 presumably she is still at primary school, in which case she may well be changing in front of the whole class, so I'd go down the crop vest top route. It would be very embarrasing for her to have to ask to change elsewhere because she wears a proper bra.
May I suggest that you make sure you get ones that have a doble layer of fabric! M&S are, as are Matalan. The single thickness ones show through their little buds and its not attractive! Especially when they've got a school blouse on. The Matalan ones come in a set with a pair of boxer shorts type knicks too.
Well amazingly Mackays (only clothes shop in town) came up trumps with a crop-top style bra with a double layer of fabric and a fastener at the back. She tried it on and put her top on and hey presto, it does the job! Not too fussy or girly either. And at £4 definitely comes in the "affordable" bracket.
My dd (11) hates the idea of 'proper' bras; far too girly for her (for some reason she particularly loathes the tiny ribbon bow between the cups, thinks that it would show through her tops). So it has been the crop top route for about a year now, and they do the job very well and are a lor more comfy than proper bras. She is still only small so hopefully will be able to carry on with them for a while.
Strangely enough, I have found that Primark do really good crop top/knicker combos for about £3. The material is really thick so you can see nothing, and washes really well, and the fabric has got a lot of 'give' to it. I have also tried Tammy Girl but the fabric is so cheap and nasty, and they are a lot more expensive. I also hate going into Tammy because the rest of the clothes are so tarty!