Need To Upgrade TV

You should be able to get a 40-55" TV for under $300.

Your issue is gong to be finding one with RCA inputs.
Almost everything now is HDMI.

You might be able to "upgrade" your DVD player to Blue-ray, that should be backwards compatible to "standard" DVD and also have HDMI output.

Curious what the above member experienced with TCL.
I've heard nothing but good about them and what a good value they are, including from our son who works on servers (like me) and builds high end gaming systems (unlike me for the past 20 years) sometimes using multiple TCL 4K TVs for monitors.