I use an Intel Mac mini with a big OWC RAID array as my home server. I previously used a NAS (Drobo, in my case) and had found the mini with lots of attached external storage to fit my needs much better. There are certain things that don’t work well on a network share (Photos and iTunes libraries, for example). Having them directly attached to a Mac gives me confidence that I’ll have a full local copy of these. The fact that my big pot of storage is directly attached to a Mac also makes online backup much easier. Just install Backblaze and pay for one of their unlimited storage plans. IMO, a Mac mini with sufficient attached storage makes a much better home server solution than a NAS.
That said, I have never found Time Machine over the network to be reliable. This has been true whether the target was a Time Capsule, NAS, or a network share from another Mac. I’ve switched to Arq for my network backups. It’s been far more reliable and consistent for me so far.