On XBOX, any monitor with an HDMI port would run. Since Xbox One runs at 1080p, you’ll need an HDMI output if you want to play it on a tv. Since HDMI has become an industry-standard, nearly every modern tv, as well as almost all modern computer monitors, has an HDMI port. A display with a minimum resolution of 1920 x 1080 should suffice.
If you’re going to play Xbox, we suggest getting a monitor with a 1ms reaction time and a 60hz refresh rate. Higher input lag values are much more significant than response time, but displays usually have lower input lag. When the game mode is allowed, many modern televisions have excellent input lag times