Your options will depend on many things...
- How much storage is needed?
- Is RAID important to you?
- Is power usage a concern?
- Noise level?
I don't know how demanding photoprism is, but you could probably do fine with a refurbished i5/i7 Dell Optiplex or similar, with one or more SSDs added to it. If money is really tight and storage needs are high, you could go with mechanical drives instead.
The problem with enterprise servers is that are generally very loud and use a lot of power...not unlike adding a second refrigerator to your environment. In my opinion, they're not worth it unless you have a specific use case (training for a career, etc.).
Amazon typically has a few vendors that specialize in refurbished Optiplexes and/or HP Elites in small or ultra small form factor sizes.
A word of caution about these refurbs though...the memory and storage they include are often dollar store brands (Kingfast) that I wouldn't even trust for a child's PC. It's worth purchasing your own after the fact.