Applying for private schools: ELC, Primary or Secondary? Plus other questions

[LionsandBears]

I've started researching schools in the area we want to move to. DS3 will be starting prep in 2019. I have no idea about public schools yet, but most of the private schools are ELC - 12. Assuming money was no object (ie, we won lotto), is there any benefit to enrolling a child in a school at 3yo kinder or primary, as opposed to year 7? Would a Montesori program be better for pre-primary? Or just normal kinder?

The schools have some great facilities, so it's tempting, but is there any value to the cost? Reception year at a school like Haileybury is $15k p.a., excluding uniforms etc.

DS is nearly 6 months old, so it's too late to apply for some private schools for primary. I'm just wondering if I should apply for primary for the ones I'm interested in and if we decide to go public, then if we can delay the application to year 7. They all seem to be variations of Christian schools (Anglican etc). We're not Christian or alumni, so that reduces our chances anyway.

At what stage have people gone on schools tours? Before or after submitting applications? I'm wondering if we do school tours this year, with a babe in arms, or if we wait a few years and see what the schools are like at the time.....

Am I overthinking this?

While I'm here, does anyone know of independent, non- religious schools in Bayside Melbourne? Any recommendations?

The schools I'm researching are Haileybury, Cornish, Peninsula, Woodleigh and Mentone. Any feedback on these would be great. What about Catholic schools in the Bayside area?

DH isn't a fan of the idea of private schools or religion, so it's going to be an interesting conversation anyway.