If the cable box has HDMI out and the TV has HDMI in then that is the best way to connect them. You then select that HDMI input and leave the TV on that input. The TV remote will have a button labeled source or TV/Video. You will then change channels with the cable box remote. Most cable box remotes can be programmed to turn your TV on and off and adjust the volume so you only need one remote.
If the cable box doesn't have HDMI then I suggest you get one that does from your cable provider. Without that you won't get an high definition picture. Much better than your old TV.
Next best would be to use the AV output of the cable box to the AV input on the TV.
Worse picture would be to use an RF cable box out to the antenna input on the TV...