Mike wants to expand the range of his television by streaming via the internet. Leo says that since Mike wants to play internet radio through his home theater system, the Chromecast Audio would be the best option. He can then browse to the internet radio station (if supported) and then connect to it. Roku has a lot more stations available, but if he has to get a website up to stream with it, then Chromecast is the simplest way to go. If he wants to connect the computer to it, then using Miracast would work.
At $35, Chromecast is a better option. Using his smartphone with Chromecast would enable him to use TuneIn or iHeart Radio to listen to streaming audio, and then Chromecast straight over to it.