The newer Roku devices all come supplied with an HDMI connector and thus require a HDMI connection to a TV. Although I would suggest that buying a new TV is probably the easiest and best solution, there is the alternative route of using an HDMI Converter box. (avg. price $20) These boxes essentially convert HDMI signal to composite signals. (reduces video quality). Here is a link for some preliminary research on them. https://www.top5reviewed.com/hdmi-composite-converters/
You basically plug the HDMI connection into the converter box and then connect the colored cables to your video and audio RCA ports of your TV. (the old style yellow cable (video), and white and red cables for audio)
You would probably be surprised how inexpensive some newer TVs are though if you want to get the most from a streaming device. Or of course you could buy a RokuTV that already has the Roku OS integrated into it. My two cents is that I prefer a seperate TV and an attached Roku device personally.
Roku Community Streaming Expert Just another Roku user... I am not a Roku employee. Insigna RokuTV, Ultra 4660x, Premiere+ 3921, Express 4k+ 3941