Thanks for your interest in the LG TVs. The highest resolution prior to the introduction of the 4K TVs were the 1080p TVs but the only source other than your computer capable of delivering the full 1080p signal was and still is the Blu-Ray DVD. Your cable box only gives you a 1080i signal which is not visibly different from 720p, so if your mother chooses not to have an HD cable box, there is no advantage to getting a 1080p with one exception, she can still get a great picture using a good internal antenna which will give her local channels in full 1080p quality!
Her DVD/VCR player will give her 480p when playing DVDs and maybe 360p if not less when playing VCR, so again, a 720p would be the better choice given her sources of content. Remember, the picture is only as good as the source!

Hello David,
Thanks for your interest in the 32" 720p/60Hz HDTV. Unfortunately, there is no way to connect headphones to this unit. Sorry you were mislead into believing that it has a headphone jack on it. The TV does not have any audio outputs on it. IFV