Bookshelf speakers for classical music

I don't know any speakers that will stop working when you play classical music. 

You need to borrow a few pairs and try them at home. That is the best advice you'll get. 

Try fritz

I think classical really sounds good with wide, uniform soundstage. Maybe JBL or Kef.

Not much to go on, but here's a nice pair of Silverline Minuet Supreme Plus in your price range.  Great sounding monitors that don't require gobs of power to sound good.  Best of luck. 

https://www.ebay.com/itm/283583900981?ul_ref=https%253A%252F%252Frover.ebay.com%252Frover%252F1%252F...

https://www.ebay.com/itm/283583900981?ul_ref=https%253A%252F%252Frover.ebay.com%252Frover%252F1%252F711-53200-19255-0%252F1%253Ficep_ff3%253D2%2526pub%253D5575084939%2526toolid%253D10001%2526campid%253D5338381866%2526customid%253Dfd9d0170-cad3-11e9-8c3c-366639333233%2526icep_item%253D283583900981%2526ipn%253Dpsmain%2526icep_vectorid%253D229466%2526kwid%253D902099%2526mtid%253D824%2526kw%253Dlg%2526srcrot%253D711-53200-19255-0%2526rvr_id%253D2092424250874%2526rvr_ts%253De08284f716c0aadb22a5e56efff3945d&ul_noapp=true

I remember an ad for the Rogers LS3/5A showing them placed on a bookshelf. This was back in '76, when they were only $450 a pair! Wish I had bought a pair or two then! Now look at what they cost! Maybe I was lucky to snag a pair for $960 ( from Lithuania, of all places!).