I'd suggest subscribing to YouTubeTV, then add things you want it to keep to your library. The DVR there seems to be totally unlimited, it supports accounts for each family member, and as shows and movies get broadcast, they're added to your library. I've been really impressed with it over the last couple months.
I'm using an LG smart TV to watch in one location, an older TV with a $50 Roku stick in another spot, and my web browser on my computer when I'm mobile. It's slick - TV is just an app, and it's portable too.