My single greatest requirement for cutting the cord was to ensure dvr capability to record Young and the Restless for the wife.
I have had great success with this:
https://www.tablotv.com/ as the dvr.
http://www.newegg.com/Product/Product.aspx?Item=N82E16815150324&cm_re=Tablo-_-15-150-324-_-Product
And the Mohu family of antennas.
http://www.gomohu.com/ Also from newegg or Amazon.
I use the Amazon FireTV as the viewer. Also has apps for most of the content channels that you mentioned. But, you would need subscriptions. The FireTV, I would say is similar to a Roku, but I prefer having the cat5 connection over relying on my home wifi.
25mb package would be plenty, that's what I have, and rarely actually get that speed since my ISP blows. We use Amazon Prime Video, Netflix, YouTube apps for the majority of our viewing in addition to the Tablo.
1 downside is that grandma/babysitter never can work the tv after the kids go to bed. While they're up the 4 and 10yr old run the controls. So, we get home and grandma is still watching kid shows. Lol