The PSU is critical, a faulty one can brick other components like expensive GPUs.
I suggest replacing the used PSU of questionable quality with a new one from a well known brand.
I agree. It's making me feel like I should just go with my original idea. After putting all the parts together, between to two different rigs, there's only a $200 difference and with the first rig, I would feel more confident the parts would be better quality.