Best Quality 42"+ TV under $500?

My mother has been in an accident and will be somewhat bed-bound for a short time, so we are looking for a cheap TV that can be set up in the bedroom.
We want to let her keep it as her main TV afterwards, so would prefer new or factory second rather than secondhand.
Doesn't need to be a smart TV or have built-in DVD. Just looking for at least 42 inch, preferably under $500, LED better than Plasma for us, with at least 1 year warranty. Had bad experience with Soniq.
Found some good ideas but with brands I haven't heard of - Palsonic, Changhong. Are these okay quality? If I get a 3 year warranty, does it even matter if it's not a well known or super high quality brand?