Synology and QNAP are the two big names in NAS. I prefer the Synology. A number of us here use them for Time Machine backup. You don't need super expensive one.. even second hand model like the DS218j, a couple of years old, would be fine. They don't change a lot year on year. The current one is DS220j.
Synology use model numbers that are logical.
DS is disk station
2 means two bays (4 for 4 bays but can be a lot more with add ons.. so gets confusing)
20 is year of introduction.
j stands for junior.. ie bottom model with ARM processor and fixed memory. Any of them with + or Plus on the name is top model with x86 like Celeron and more memory slots. For just Time Machine the bottom models are fine. If you want to use a NAS for streaming movies etc.. then plus models are a lot better.
I recommend people buy a 2 bay model rather than just single disk.. you can buy one hdd now and add another when you fill the first drive if you decide to maintain the history over long periods. Alternatively a USB drive could be used to backup the NAS then wipe the internal drive and start over. This gives you an off line backup.. no bad thing in the world of ransomware.
Typically people buy 4-8TB disk size. More than adequate for average home usage. A NAS and a proper NAS drive will still come out expensive.
Looking at a couple of current articles for NAS and Time Machine.. they almost copied each other.
https://appletoolbox.com/the-best-nas-drives-for-mac/
https://www.macworld.co.uk/feature/best-nas-drives-mac-3674321/
Both put WD cloud drives at top of the list.. I can understand the choice but not sure they are the best solution.
We would only be using it for safely and securely backing out our laptops.
It is much cheaper to just buy 2 USB drives and plug one into each of your laptops. It also works better with Time Machine. If you don't want the hassle of unplugging and plugging a USB drive all the time because you are using the laptop on the road buy a charging USB hub suitable for your laptop and just leave the drive plugged in permanently on your desk. It will backup when you charge the laptop. Portable drives are fine for this purpose.