Connecting to DirecTV Streaming

Those must be very old TVs if they don't have an HDMI INPUT.

All streaming devices have HDMI OUTPUTs. You'll need some sort of converter to change the streaming device HDMI OUT to an INPUT that's compatible with your TV, most like COMPOSITE VIDEO and analog AUDIO. 

Streaming devices are output by HDMI. You need adapters to A/V the red/white/yellow plugs or whatever older connection your TV uses.

But if TV has no HDMI input, then it is very old and I would be concerned about the quality of picture on such an outdated TV.

Not sure what size tv you like, but many retailers sell 32, 43 inch tvs for 75 to 150 bucks. At least they have HDMI ports--which would be an upgrade over what you currently have.