In my opinion the public school seems like the best option, at least for elementary school. My family sent my siblings and I to public school for elementary school because the school in our area was good and there was a good community even if it was more progressive. They all seem fine and have had great moral and religious formation at home and in a good Catholic high school which seems to be the best time as that is the time peer pressure becomes more present and more moral issues come up(sexuality, drugs and alcohol etc, abortion). Having a strong foundation in ethics and moral theology as well as friends who believe and follow similar morals is most important as they begin to grow into independent adults and are able to understand those issues.
Also, because it’s elementary school there isn’t a ton of sex Ed and that type of thing that may teach your child things contrary to your faith, although it depends on your school district. You could also use that those years of no tuition to save up for a Catholic middle school or high school if there are good ones where you live and you think it’s a good decision. From what I have heard from friends though, parochial schools aren’t much better than public when it comes to instilling Catholic or Orthodox values into your children, although the education is sometimes of a slightly higher quality. As long as you provide strong formation at home or at your church, I doubt the Catholic school will be a much better influence
I would not recommend homeschooling unless you had a strong community of homeschoolers near you who you could meet up with a few times a week. A social life is so important for a child’s development and it’s especially hard to get that as an only child homeschooling without a group. You can teach them religious education at home