Best NTSC TV, ~32 inch, to hang on wall

I am looking for a good TV for an NTSC cable system with a marginal signal. Some the channels are better than others. It will not have a DVD box or any gaming connected.... just AC and one F connector for the analog cable. The cable is provided at her apartment. Digital is not an option. Over the air is not an option.

If a 120 Hz TV could improve this kind of signal, I would go for it. But I suspect that the value of 120 Hz processing is only for digital signals. So more money for a better picture from this analog cable system could be worthwhile. Features that improve only digital signals will be of little help in this application.

A feature that remembers separate volume settings for each channel could be useful.

It should be maybe 32 inch. I intend to hang it on a wall, so thinner is better.

It's for my mother, so she will probably be watching 4:3 programs stretched to fit the screen. Very little actual 16:9, although some programs with 16:9 content come in at 4:3 with black above and below. It would be nice if that adjusted automatically. I would rather see black added by the TV on the sides of 4:3 content, but she likes the screen filled.

Are there any suggestions or comments from somebody who has had some experience with NTSC cable in the past five years?

Thanks, Steve.

Yes, the local broadcast channels (x.1 only) are on the cable as QAM. The channel numbers are weird; those channels are accessible more easily by starting at channel 2, and scrolling down through the enabled channels. Those pictures are much better than the corresponding channels they send over NTSC..

The majority of channels (A+E, USA, TNT, and a bunch of others) are only in NTSC. I have to feel that some makers do a better job of producing a less-inferior picture than others when fed a much-less-than-perfect NTSC signal.