If its the displayport on your current monitor you're worried about keeping, then you may have better luck looking for a USB-C connection in your price range, which can output DP signals and connect with a conversion cable or adapter. Otherwise, I would do what you can to use the HDMI out. Displayports on laptops are normally associated with higher end gaming laptops, which will be 2x-3x minimum of your target price point.
The HP 15-dy2076nr is available from BJ's right now for $500, though you may be able to get others to price match. i5, 8GB RAM, and a USB-C port. You will hate yourself with anything less than that, because Windows will crawl and multitasking will be painful. I believe this is the same model I bought my daughter for school a year and a half ago and it's held up just fine. Outside of that, you may want to look at some refurbs, though they can be hit or miss.