My son goes to a private Christian school, and he loves it. I don't really have enough information about yours to offer much advice but I will try. The old school he went to wore uniforms, and it wasn't so bad. He didn't seem to mind, and it kept down a lot of the stupidity kids have today about clothes, such as equalizing the monetary differences between students. He was there because a doctor friend of the family was helping with tuition, and the school had some of the richest kids in school. And his wal-mart brand white polo shirt didn't look any different on than their Ralph Lauren ones. Plus, I could work with them to his sensory issues without him losing the "right look" kids were supposed to have for whatever reason.
Another factor is size. I know this can vary a lot. My sister's school is private and supposedly Christian and they have over a hundred kids. Although given their behavior, I would doubt any real faith-based decision making. On the other hand, my boy's old school had 23 kids, his new one has 9. This is perfect for him, as it eliminates the chaos that usually goes with a big public school and having to navigate a big school.
I went to a public school, undiagnosed, and went through 13 years of hell. Literally all I learned in those years was that I wasn't worth what the teachers scraped off the bottoms of their shoes. Glad you have a better option than I did.