Here’s all the gear you need:
How to set it up
To keep this article relatively short, I'm going to leave out some of the details.
Configure the backup laptop
First do the basic configuration for the Windows OS on the backup laptop. This involves uninstalling all of the bloatware that comes with it (pretty much anything that can be uninstalled should be, aside from required device drivers such as those from RealTek or Intel), and applying all of the latest system updates. I also advise you compress the internal hard drive, remove older versions of the system files, and use the USB flash drive as additional storage when applying system updates. While you are at it, install Resilio Sync on the backup laptop. I do not recommend installing any other 3rd party software, even things like Chrome or 7-Zip. Keep the system completely bare bones for simplicity.
Configure each computer that needs to be backed up
For each of the computers that you want to back up, install Resilio Sync and then add the folders you want backed up to Resilio. I recommend the 3 Ds: Documents, Desktop and Downloads. If you keep specialized files elsewhere (photos, videos, music, fonts etc.), be sure to add those folders as well. As you do this, copy the key (I use the read only key to prevent accidental modifications or overwrites. You may also want to use an encrypted key for security.) for each folder and paste it into a text document. Label each key with the computer/user name and the folder name. I save this document out to a file on a USB drive and take the drive with me to each computer I'm working on, but it could also be stored in a secure cloud service like LastPass or Google Drive.
Link the org computers to the backup laptop
Once you are done setting up Resilio Sync on each of the org's computers and you have a key for every folder on every computer you want backed up, it's time to link them to the backup laptop. On the backup laptop, format both portable external drives to ExFAT. I named them 4TB backup #1 and 4TB backup #2. Create a folder structure that will organize your backups. I recommend a top level folder for each computer, and inside a folder for each folder that is being backed up in Resilio Sync.
In Resilio Sync on the backup laptop, click + and choose Enter key or link. Paste in the key for each folder and link it to the appropriate folder on the portable external drive. It might take a bit of time for the folder and file structure to be read in and indexed by Resilio Sync, but after that the sync should start. If you can, plug one or both computers into the Ethernet network. This isn't essential but I find it tends to make things go a lot more quickly.
Once the first drive has finished syncing, quit Resilio Sync on the backup laptop, safely eject the external hard drive, and then plug in the second one. You may need to use the Disk Manager to remap it to the same drive letter as the first drive (usually D:). Now start Resilio Sync and let it do its thing once again on the second drive. In the meantime, take the first drive and put it somewhere safe. Ideally off-site (the further removed geographically the better, but keeping in mind you should be swapping the drives every week or so) or in a fireproof and waterproof safe locally.
Restore from the back up
Definitely check to make sure you can restore from the backup before you actually need to. One of the great things about Resilio Sync is that it stores the backup in the same file structure as the original files. You can just browse through the folders and files and open a few select ones to ensure everything looks good.
The other thing that is great about Resilio Sync is that it keeps a 30 day archive of older versions of files. So if there is an accidental delete or modification of a file, you can right-click the folder in Resilio sync, open the archive, and pull out an older version of the file from there.
My personal backup laptop with one of the backup drives mounted to the back using 3M dual lock fastener tape
Reasoning behind this setup
I've been helping nonprofits with IT for almost 5 years now, and I've tried a bunch of different systems. While there is no one-size-fits-all solution, I think this works best for a lot of SOHO (small office/home office) orgs, and especially those where cloud isn't a viable option (where cheap and fast internet is not available).
You always have to worry about power outages. I have previously used a dedicated UPS. But having a laptop and USB bus-powered hard drives obviates the need for this extra item, and keeps things simpler.
Resilio Sync is hands down the best backup app I've found. I used to recommend CrashPlan, and it's still a good app. But I like Resilio because it backs up continuously and you can easily add other devices to create even more redundancy if you wish. It has the archive feature for accessing older versions. And most importantly it keeps it's files in a readable form so even if you lose both the original computer and the backup computer completely, as long as you have one of the backup drives, it's easy to get back up and running.
Definitely let me know if you end up doing this and what your experience is with it.

My personal backup laptop running Resilio Sync to keep my MacBook Pro backed up