Cvargo82
The Roku streaming devices (and FireStick/FireTV by Amazon), require an internet connection. (content is streamed over the internet to the device).
Wifi is a local "network". (think of a router). The Roku device will connect to your network, and then will connect to the internet when actively streaming content.
Generally, devices can connect to a network in two ways. (wired and wireless). With wired, you run a network cable between the router and the device. With wireless (wifi), you do not need the cable for the device to communicate with the router (as long as the device is wifi-capable).
You do not need internet to have a network. A network is local to you and your devices. This is how you can get computers in your home to communicate with other effortlessly. However, you do need internet access in order to browse the internet and use your Roku devices. (and any other streaming device).
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As for cancelling your cable question. If you wish to receive most/all of the channels you did with your cable package, you may find subscribing to a "cable-alternative" package an easy way to make the transition. (Hulu, Sling, YoutubeTV). https://channelstore.roku.com/browse/cable-alternative
In many cases, if you have just a few channels you really watch, you may be able to just subscribe to those channels directly. (browse through the Roku Channel Store from the above link). Any channel in the Store that says "requires cable subscription or TV provider" means that you need a cable subscription or use a cable-alternative service mentioned above. (some users maintain a cable subscription and then just use the Roku device in place of their rented cable box).
However, with streaming, you may find that you really don't need any of the cable channels you used to watch and find some alternative programs and channels very similar for free on the Roku platform. There are many channels/apps like Roku Channel, Pluto, Filmrise, Tubi, Sling Free, Xumo, and many others that offer free content (with ads).
Many subscriptions are billed monthly so you can also bounce around and try to find what works and doesn't work for you.
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As for setting up favorites, etc. You can move your channels/apps around on your device in an order that is convenient for you. Also there are different ways in the various channels/apps that you can set up Favorites. (each channel/app has its own features and behaviors).
Streaming comes with a bit of a learning curve. It may not as easy as just turning on the TV and selecting a channel number with the remote. However, you will likely find you will access to things you did not find or knew existed through your cable subscription.
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A good place to start may be to visit the Roku website https://www.roku.com/, and browse through the "How it works" section.
Feel free to post back if you additional questions.