Backup services vary widely in how they set up and perform backups. For example, the totally hands-free Backblaze automatically encrypts and uploads all your important files without any input. On the other hand, services such as IDrive and Acronis True Image let you choose specific files you want from a file tree. Note that some services restrict you from backing up specific file types or using particular sources, such as from an external or network drive. Make sure the service you choose supports all your needs.
CrashPlan is completely free if you're just doing local backups, but even online backups are affordable, with CrashPlan+ accounts starting at $2/mo (per computer) for 10GB of online backup storage, and going up to $4/mo (per computer) for unlimited online backup storage and $9/mo for unlimited online backup storage for a whole household. You can check out their plans here, and try them free for 30 days with a new account.
This program is straightforward to use because there are only a few simple steps to download YouTube videos and channels. The first is that you need to copy and paste the specific URL for the video or channel that you’re trying to download. From there, you get to select the specific video resolution that you want to use. Then, just download the video. It really is that simple to get the access you’re looking for. If you want to convert the videos that’s an option too, so you may want to check it out as a free option.
In addition to the 5 GB free option, OpenDrive has one consumer-grade plan called Personal Unlimited. It costs $9.95 /month and offers an unlimited amount of storage space for your backed up files. Prepay for one year at $99 to bring that down to $8.25 /month. You can add an additional computer for $9.95 extra /computer, up to three extras for a total of four.
If you want to download as videos itself, you can use other free tools like Free Youtube Download to download all videos with a single click. Please be careful while installing this tool as it optionally installs a browser toolbar and modifies search preferences. So please make sure you read and uncheck the optional checkboxes while installing to avoid surprises in your browser. 
Many services also offer a feature called versioning. This saves incremental changes you make to files as recoverable snapshots of the file. It's useful in case you need to get back information from an earlier version or if your latest file save becomes corrupted. Services vary widely in how many versions they keep and how long they're saved. Best-in-class services, such as SOS Online Backup and SpiderOak ONE keep an unlimited number of file versions forever.