how ironic that the nomenclature has been so twisted that now we are referring to "personal cloud" storage? the idea and terminology of "cloud" storage is that it is NOT on your device/s but stored off site on someone else's device and you use the internet or other significant network to access it.
if i read the OP right, they/you would like to have access to your old movies and tv shows even when good internet access is not available. in that case you would need to store the movies/shows on local storage devices. like harddrives, thumbdrives or cd/dvd optical disks. in most cases the cheapest route for significant storage is going to be harddrive. tera byte drives are cheap these days. heck my laptop came with a 1 tera byte drive and it is a cheap laptop,
if you dont need ultra high resolution and stick with DVD quality and use some compression software to save them in avi or other format you can save tons of shows and movies on a single tera byte drive.
i wont get into the details of how to download and save to these formats as the process is ever changing you will need to look into how that is best done.
once you get what ever shows/movies you want downloaded and save to your local storage it is just a mater of picking a media player that will allow continuous play and even better the option to make playlists. i used to use windows media player for this. worked great. this was a few years ago and in order to build up cheap storage i was using 200-300 gigabyte harddrive stacked with expansion boards and several usb hard drives. when i was still in a sticks and brix we had cable tv and 5 seperate computers in the house each with an "all-in-one" video card that would play and record from the cable service. we could program what was recorded a week in advance and with multiple machines we could record several shows that were playing simultaneously. we ended up with just shy of 3 tera bytes of movies and shows that we downloaded as we transitioned out of the city life. then we took our stacks of hard drives that we labeled based on the type of shows on them and would swap them out depending on what we wanted to watch.
now a days it would be so much easier with the massive terabyte drives so cheap. the hard part will be downloading and compressing in a format and resolution that works for you.