Not a curved screen, but I bought one of these recently: https://www.asus.com/uk/ROG-Republic-Of-Gamers/ROG-SWIFT-PG248Q/
Only 24" and 1920x1080, but it suits me fine. It's a very nice display - Oolite at 144fps (G-Sync/DP) is silky-smooth! Again, no built-in speakers, but what Kal said is true. I run my sound off a soundcard into my hi-fi.
I bought the LG 34CB88-P 34" Ultrawide QHD 21:9 Curved IPS Monitor, 3440 x 1440 5ms last Christmas and I have zero complaints and it works great, not sure if this model is available or if they have newer. But I picked this up for $569 on sale and it has speakers too.
See this post for pics: http://spacesimcentral.com/forums/topic/what-is-your-current-pc-config/#post-110798
As for speakers try Creative or Logitech!
That Asus monitor seems to have jumped in price - I paid under £350 for mine. Still way beyond your budget though, Pinback. Have a look at iiyama, perhaps? I used iiyama for many years - good budget monitors. Actually, this one has pretty good specs (and FreeSync if you're running an AMD card): https://iiyama.com/gb_en/products/g-master-gb2488hsu-b3/ Currently £230 on Amazon, I believe.
I would agree with CaptianKal on this one, unless you really want to game on something above 1080p then there is really no reason to go above 24" to be honest. Plus, even if you have a 4k monitor unless you have the gfx card to push 4k at least at 30fps your wasting your money.
I purposely bought my setup to do 1440p or just the step under 4k. Why? Because the tech really isn't worth it right now for gaming in 4k and it costs way too much for very little return, maybe in another 2yrs 4k will be solid and worth it.
To be honest I have to hunt a lot for fixes or patches that will scale older games up to 3440x1440 or run with using smaller resolution and seeing black bars on side or bottom. Higher aspect ratio monitors are definitely only good for productivity and 2015yr or newer games.