do I need to replace it with the same capacity, 2TB?
No.. any capacity above about 3x the disk capacity of all the Macs that backup. And then anything above that.
Synology DiskStation DS118 Mini Desktop NAS
Wow.. that is a class above what I was thinking.
The model I recommend is DS220 (it comes in flavours, j and plus with fairly wide pricing difference)
The cheapest is J so DS220j but if you can still find a DS218 it would also work.
There is a one bay model but the price for 2 bay is not a lot extra.. the actual controls and board etc are identical but the 2 bay allows you to add another disk later.
2TB SSD
I would NOT buy an SSD for a NAS. Let me explain why.
SSD are expensive in large disk sizes. The cheaper versions have file write limits well below that of normal hard disk. Backups do use a lot of writing and rewriting of small files.. so SSD while fine for normal home use.. are not really suited to this job.
A good backup drive like Seagate Ironwolf or WD Red have long warranty and come in sizes from 1TB to 16TB or thereabouts. I stick to around the 8TB size. But you could by a 4TB if it saves a lot. Not really worth buying under that size.
More important.. over a network.. the rate determining step is gigabit ethernet. It has a limit of lets say 115MByte/s .. whereas even a slow NAS drive can do 180MBytes/s. There is some speed gain using SSD for small files.. as it is much less efficient writing file tables on the disk.. and Time Machine cannot really manage backups much faster than 40-50MBytes/s and much slower when it is lots of tiny files. In other words in this situation.. an SSD gives no speed gain whatsoever.
On balance.. if you want a small compact low power consumption NAS the DS118 with 2TB SSD would be super.
I would still buy the bigger unit myself.
A DS220j with 8TB NAS drive is around the same price I guess.. check amazon etc.. just as fast in this context.. bigger and although very quiet not as good as the smaller unit. If you run out of space though you can buy a second drive and put it in making the backup 16TB..
dealing with a guy who is 76
Keep well and stay safe.
Happy to help if you need more details on doing anything.
I am only 67 but the doctors took 15 years off my lifespan with bone marrow transplant when I was 40 so I didn't die at 41. So I feel about 82. Better than 41 so not complaining.