I think the most important thing is display panel and refresh rate. There is not a total "best monitor" for reducing eye strain but if you buy a monitor for with an IPS or VA display panel and blue light filter, that would be enough for reducing eye strain when using monitors.
My advice would be to choose a larger monitor than 23" for console gaming. You can check out ASUS or BenQ monitors in range of 200$ - 400$ with Full HD res. Here is a guide for choosing the best monitor for PS4 and I think you can use it.