Most of budget computer displays on the market have ventilation holes on the back. Its hard to find a budget display (Under $200) with minimalistic design, ie with no air holes like smartphones are. I thoght may be there are some brands that has a tendency or tradition to produce such monitors? If not then may be you could recommend some budget models?
Monitors, like all electronics, produce heat. The cheapest way to get rid of this heat is to provide a path for the hot air to rise and cool air to flow in and across the device.
The only monitors I have seen without ventilation are portable ones like this. It is currently $170 when you apply the coupon. If you search "portable monitor" you will find plenty more like this.
I would highly recommend using separate speakers. You are not likely to get anything worth listening to out of a "budget" monitor. External speakers are both higher quality, and cheaper.