Some things I discovered going down the I-130 route with my children (I am US Citizen)
1. While your child(ren) cannot age out for the I-130 process, if we then immigrated after my child(ren) was 18, then they would not be eligible for the "instant citizenship" that is referred to, and they would not be eligible for the N-600. As that has to occur before 18. They would have to go through the PR-> Citizen conversion like any other adult.
2. N-600 and N-600K are similar but different. They are both applications for certificate of citizenship for under 18s, which is needed before getting a passport or a SSN, if the child was not born in the US.
N-600 is if you reside in the USA
N-600K is if you do not.
For me, the process of N-600K was the right one, as we ended up deciding not to immigrate.
N-600 and N-600K can only be done for under 18's.
The reason I would consider applying the children first and with an N-600K is that
1. Them all being US Citizens provides added weight to the I-130 for your husband
2. N-600K costs about $1K USD vs (I-130 + N-600) which is about $2K USD (if I recall correctly). With 5 kids ( I think you said) that's a huge possible cost for you.
But it depends on why you want to immigrate, and when. And yes, doing the I-130 for all may be the best and quickest course of action. The children will receive "instant US citizenship" as children with PR and US Citizen parent. However proving it when applying for passports and SSNs _might_ be harder, and then N-600s might be needed.
Regarding visas/ESTAs, the US frowns upon people applying for visas with the intention to immigrate. ESTAs can get denied, and even tourist visas can get denied.
I just had a look at some of your previous posts, if it's an internal transfer and his company files for the visa, they will also be involved in the filing for visas for your children, as dependents. Once in the country then you can apply for PR for all. And then if you need to, you can apply for N-600s. You may not need N-600s if you can prove residency.
As I'm sure you are already finding there are multiple routes for visas and citizenships. Good on you for doing the research before applying for anything. I had no resources when I started, so this forum is an amazing help.
I'm not one of the lawyers in this forum. I am someone who started the I-130 and then got screwed by the pandemic and embassy closures, and ended up going to N-600K for my children. My husband's I-130 is still sitting in the system in case we want to pick that back up again. All I can share is that I wish I had just done the N-600Ks for my children when they were young. I had family circumstances that prevented it, but that's absolutely what I should have done.
Good luck with your decision making.