In case you did not invest already in a NAS. I had to decide the same question.
I bought a thunderbolt HDD enclosure and attached it to a Macmini Server. This way I can format all the drives in HFS+. In case you have an old Mac you can run macOS server on it and I would prefer this solution!
Regarding Backup scenarios there are advantages and disadvantages to both.
Timemachine can only backup your system disk or everything. This means that in some cases you would need a massive networked volume to backup. This would usually require RAID and RAID and backup are incompatible! But Timemachine keeps history and you can easily browse the backed up data.
Carbon copy is an excellent programme. You can backup whole drives or folders. It is highly customizable. It has a function called SafetyNet which keeps history, but it is much more difficult to browse and recover.
I use Timemachine for systemdisks and Carboncopy for secondary internal drives. This way I do not need to build RAID volumes to be able to backup multiple drive machines.
I backup to networked volumes. Server, switch and 4bay thunderbolt enclosure are attached to an UPS.
NAS are great, but when apple updates something you could get problems with compatibility.
Since Timemachine is a proprietary technology I would try to do without NAS and go with an HDD I can attach to a Mac and format in HFS+. Backup solutions should be as simple as possible and the complexer the setting, the easier something gets corrupted. NAS means usually RAID, ext3 and so on. Too many possible points of failure! Too many things which could get corrupted.
In case of a Carbon Copy backup to a networked volume on NAS you would backup to a non HFS. This can cause problems especially with metadata, permissions, ... Timemachine backs up to sparsfile, CCC mirrors your data to a volume. Timemachine sparsefiles can get corrupted, CCC might loose permissions, metadata.