The "red, yellow and white" is a composite connection, the yellow for SD video and the red and white for stereo sound. If your TV has these connections then a Roku will hook up to it.
Some older TV's have only a coax input. For these, you need to get an RF modulator to switch the composite connection to a coax connection. Or, some older VCR's will let you connect in too.
I originally started with Roku because I needed to hook up to an old tube TV and the AppleTV requires an HDMI in.
Tip: If you are watching on an old SD TV, you can save bandwidth by backing down your download speed to three dots. (Click 5 times on the top button of your remote, then three times on rewind, and twice on fast forward to pull up the interface.) On a tube tv, you won't see any difference.