Moved to college and need a monitor / TV what do I buy?

So I’m moving to college in the morning. My desk top is being shipped to school. At home I have a TV and a monitor. I need to consolidate/ buy new at school. I’m looking for something with

2+ hdmi spots

32-42 inches

Under $800

And I’m a little confused. My current monitor is a 32in LG tv of sorts. It caps my computer at 60hz but when I play games I can exceed it and it feels just as smooth if not smoother then my PS5 on the living room tv which is a newer and better 80+ in TV that does run 120hz

Anyways id kike it to stay that smooth