What type of tv can we buy that will work with basic DIRECTV service and an older DIRECTV receiver?

My mom doesn't want to pay for the DIRECTV HD signal or to upgrade to a new DIRECTV HD receiver. She just wants a newer, slightly bigger (about 22" - 26") tv. She is loyal to her old DIRECTV/TiVo box and just wants to retain basic DIRECTV service. I don' t know if there are any TVs out there that will work with this older equipment and still give a decent picture. Seems like you can't even buy a non-HD tv anymore. Are the new TVs able to be "backward compatabile" kind of like computers are? Any suggestions about what we can buy would be greatly appreciated.