Hello,
You should be able to watch cable on an old TV. Is the TV standard definition? The only thing is that if it is SD, you will get black bars on the screen, because almost all stations are high definition and the cable boxes are now almost all high definition as well.
Some of Spectrum's Guides have a menu setting in the Settings options where you go to adjust the output resolution of your TV. If you get an HD box and you have a standard definition TV, you will want to set your Output resolution to 480p and deselect all the others. If you have a Menu Output setting and you have the old TV hooked up to an HD box, you will need to change the menu output from 16x9 (The HD setting) to 4x3 (The SD setting.)
If you purchase an HD set in the future, you will need to also have an HDMI cable or Component Cable for an HD picture. They run about $20 at any local electronics store, AND you will need to change your Menu Output resolution to 16x9 and your cable box resolution to the highest HD setting that your TV supports, generally 1080i
Spectrum employees, does Spectrum rent out SD boxes anymore?
Satch