Your laptop probably won't support any 4ks in that price range, since those would be mostly Korean monitors (though check on ebay to be sure). At 4k, I would recommend at least 30inch diagonal, but that depends a bit on your personal preference and tolerance. You could find a 28 inch at 4k within your budget. There are a lot of options, and to be honest, for poker, it doesn't really matter that much how good the picture quality is. Just make sure the ergonomics are decent (swivel, tilt and for me most important is height actually). Also don't buy a TV, as they might not have the right refresh rate, which is one of the few import factors for when selecting a monitor.
I use this monitor:
https://www.amazon.com/Samsung-Monit...msung+34+se790 and this monitor arm with my laptop currently:
https://www.amazon.com/AmazonBasics-...ds=monitor+arm. This is over your budget however.
When I was buying, this was my preference:
https://www.amazon.com/BenQ-32-Inch-...rds=benq+32+4k
But it was out of stock at the time I needed it. Hope that helps.