As the board's resident K-12 policy expert, I'll give you my thoughts on all of them, or at least the ones I would consider.
St. Andrew's
Its K-12, with the elementary school in Jackson and the middle/high school on Highland Colony in Ridgeland. It has an excellent reputation, but it comes with a lofty price tag. If your children lean toward the humanities, its even stronger. They marticulate several elite college students every year. Is not uncommon to see their graduates choose Duke, Vanderbilt, Rice, as well as a couple of Ivies and some good small liberal arts colleges. They are the only Jackson area private school to play sports in the MHSAA, now that St. Joseph is moving to the MAIS.
Jackson Prep
It's 6-12, but First Presbyterian Day School is a de facto elementary school. It has a good reputation, and has great opportunities for sports as well as performing arts. They are as close to what I call as a "Bayside" school, where as its not uncommon to see a linebacker performing in musical theatre or a star pitcher on the newspaper staff. I think Prep has the best overall faculty. I'm a little worried at their debt load. $12 million in revenue and $7 million in debt. They just lowered their tuition and opened up more SIS aid - thats a sign that they are worried about it too.
Jackson Academy
Northeast Jackson's de facto community school. Its K-12, has a strong endowment, but is struggling to find students as Northeast Jackson is running out of kids. Its not a convenient location for Madison and Flowood families, but they are trying to recruit more from those areas. If your child is more tech/engineering focused, I think they are stronger there, although they have good humanities and performing arts. Sports aren't what they used to be, but its not for lack of trying. I think their target student base is drying up.
Madison Ridgeland Academy
Fastest growing, largest, mainly because it has become the area's premier athletic private school. Its K-12 and they are healthy financially. Academically they are weaker than the above schools, but not bad. Their main competition is Madison's public school system, which helps them when competing against other area private schools. Their problem is that they are kind of locked in with no room to expand. They own some property at Reunion and Bozeman that they could build an elementary school and change their current location to a middle/high, but it hasn't materialized.
St. Joseph Catholic School
Has a great location but just hasn't taken off. Its 7-12 and Catholic scares some potential families, although you do not have to be Catholic to attend. They have a ton of debt but are supported by the Diocese of Jackson so its not as big of a problem as it could be. Sports are moving to the MAIS next season, so they should be better. It will be interesting to see if this attracts more students.
Hartfield Academy
A huge turnaround from a decade ago when this school was University Christian and a joke. Its the most Christian of the private schools - and its covenantal - which means all families must agree with a statement of faith. UCS had the reputation of taking in whoever got kicked out of Northwest Rankin or Brandon - Hartfield has shed that and has grown significantly. Their problem is that their campus is too small. Its K-12 with I believe K-3 at the Pinelake campus and 4-12 at the Luckney Drive campus. They are going to have to expand some way. They built a nice new addition and the auditorium/multi purpose space was too small the day it opened. Academically, its about like MRA, but its better than the area public schools. They don't have the performing arts and humanities that others have, but if you are interested in a Christian school with chapel and character building, this is a good place. Their turnaround has hurt Jackson Prep in my opinion, but they made a mistake in renovating and building on and not building all new on East Metro Parkway. This would have allowed them better access to Brandon/Pearl, who has East Rankin and PPCA, but Im not including them because they are jokes.
Hartfield has $15 million in debt against $11 million in revenue. I think they could have built a new campus on that donated land for $20 million and increased revenue to $15 million and end up in the same place.
I'm going to add this - they aren't there yet, but Canton Academy could be a sleeper. They are close enough to Gluckstadt to be attractive and there are a ton of rooftops in Gluckstadt with kids. I think they could learn from Hartfield. Change their name, change their focus and they could grow. They already have SACS accreditation (UCS did not when they changed to Hartfield). I'm not sure the current board of CA is interested though. My prediction is that if they don't do it, someone else will see this prime opportunity and jump at it - either a church, or an existing school will expand into Gluckstadt.