I spent a while researching 4k monitors a few weeks ago with a strong intent to buy one.
Ultimately I went for a 25" 2560x1440 monitor for ~$300[0] and it's amazing.
The problem is, a good SST 4k monitor with an IPS panel that runs at 60hz and supports 4:4:4 with a low input lag is going to be impossible to find at your price point.
Also keep in mind PPI. A 2560x1440 display at 25" is 117 PPI. A 27" 3840x2160 monitor has 163 PPI. That is a MASSIVE difference and at your price point that's about what you'll find unless you start looking for TVs and use them as a monitor.
The problem with TVs as monitors is they tend to have HDMI 2.0 ports and no display port, so you might have a hard time connecting it to your laptop unless your specific model supports HDMI 2.0 out of the box.
Their specs also tend to be a lot worse and to get a "good" one will likely run you double/triple your budget.
Then of course there's the whole size problem. A 36" 4k monitor is 122 DPI which should be awesome at 100% scaling but at 2-3 feet away you're going to have to move your head around like a maniac just to see each side of the screen.
[0]: http://amzn.to/2jF3WHp
