Glad you clarified because no, you can't turn on the TV and see "Castle" at 9:00 on Monday on network TV when it's initially being broadcast fresh and new -- not on Roku, at least not that I know of!
You do have to have Internet service. Roku is a streaming service of shows and movies but does not provide your local network affiliate channels; you can see their shows only eventually, when they are finally done broadcasting them and make them available via streaming. Same idea as waiting for a show to come out on DVD when the broadcast season is over on its network.
You get a huge catalog of what's in their library of TV shows and movies, so for instance you wouldn't see this whole season's episodes of "Castle" until the broadcast season on ABC is over and it's made available as a package on Roku probably next spring or summer. Some shows may be made available sooner, as the season progresses; I'm not sure. I know that ones we want to watch sometimes take many months to update with new episodes.
You can get Netflix, Amazon Prime, PBS streaming, and other channels, some of which are cool and some of which are freaky.
We use the Netflix a lot and the free services such as PBS streaming on there (again, not "live" PBS from the local affiliate station, but PBS programs that are done on TV and now are available to stream). But it can be quite a wait. For instance, we watched all of the first few seasons of "White Collar" months ago, and so far, the following seasons have not yet been made available for us to stream via Roku/Netflix. We could order the DVDs in "hard copy" format and have Netflix mail them to us (it's a rental, not for keeps) but we'll probably just wait for the show to turn up on streaming.
One thing to know is that HBO does not let Netflix stream any of its shows so if you like HBO programming, it's not on Netflix, period, so I'm told. It may be available by DVD but not via streaming.
I would not give up my local TV news and replace it utterly with streaming. We do not have cable or satellite but use an antenna for local TV. Since antenna TV is not an option for you, maybe look around at how good your local stations are at broadcasting over the Internet. That's where I go for urgent weather alerts. But Roku isn't for you if you like to keep up with a TV show week by week as it's broadcast -- you'd have to wait quite a while for it to turn up on streaming. Some networks do make things available online in full episodes for a short time after initial broadcast! Not sure if ABC does that but NBC does it on Hulu for about one week after things are first broadcast (then the show disappears). Or at least NBC used to do that -- havent' tried Hulu for a while.
Hope this helps.