I just got through setting up a new smart TV to act that also acts a a second monitor for my new desktop computer.
The 24" Class LG smart TV cost me $127 delivered. It is attached to a simple flat panel HDTV antenna, which is situated behind a sofa, chich is close to a window. Here in Houston I normally receive ~120 over the air broadcast HDTV channels. Excluding foreign language, religious, and shopping channels I recieve a good 30 channels of interest to me. The TV also connects to my Wi-Fi and can directly stream program information from a multi of free and pay sites on the Internet. It also connects wirelessly with my computer, so anything I can play or stream on my computer can be played on the TV. This includes DVDs, because the computer has a DVD player/burner with movie playing software.
If you do not want to buy a new smart TV, various devices like Roku, Fire TV, Apple TV, Google Chromecast will attach to an HDMI port on your old TV. If your TV does not have and HDMI port, I'm not sure what you need.
With taxes my Internet only service sets me back $65 per month, I have no pay services on top of it. I do not have The Weather Channel or CNN, but if there is a breaking news story that is not covered on the OTA stations I receive, I search online for a TV station close to the hurricane or event and usually find they are streaming the event live online.