Netflix or similar. I'd like to get a service like this, but can I put it straight to my TV via phone line?

Not as direct as you think.

You need broadband Internet first. To get that you use a modem that plugs into the phone or cable line, and provides at least Ethernet (not to be confused with a phone line). Yes you need to subscribe to Internet service, separately from the content service.

If you have a smart TV, you can plug it into the modem directly, or may need a router.

If your TV is not a smart TV, or an older generation smart TV that doesn't support Netflix, you need to add a box such as Roku or Apple TV, which connects to your Internet and TV, or use your computer connected to your TV.

If your tv has "Smart" functions like many new ones do, you should be able to get netflix or similar widgets to play on it. Also some blu ray players can act as a proxy for this service. If your TV or blu ray has a LAN connection or Wi Fi you should be good to go. Failing that you could look at the micro Android PC market, MK802 etc these (i believe) work with netflix.