so I have 2 children, all 3 of us are legal residents (10 year green cards). The kids are minors. I'm going to apply for naturalized citizenship and "should" become a naturalized citizen early next spring.

It's my understanding my kids will be become citizens automatically when I do based on derived citizenship. Is that correct?

Do I have to submit anything special for them to have proof of citizenship? In other words if I apply via N-400 and list them, will they get 'proof of citizenship' when I'm approved? Will they get something to take to the post office to get a passport?

Or . . do I need to apply an N-600 to get them a proof of citizenship document?

thanks so much in advance for your help

My daughter [K4] just recently got automatic USC but I adopted her. She had to be in my physical and legal custody for 2 years.
I applied for her passport [$82] for proof of USC.
They do their own checks on citizenship eligibility.
They held her passport application for 9 months until the custody requirements were met.
Didn't want to pay the $420 for the n-600 as I wasn't sure it would it would "fly" or not. No refunds.
Will do so now tho.
Different than your case tho.

Agree... Once you get Citizenship, apply for a US Passport for yourself and your children. Your natz certificate along with their BC's showng you as their mother should suffice (with a marriage certificate if that is what is needed to bridge the names)...

After you get the passport, I strongly suggest you file N-600's for them so they can get a Certificate of Citizenship.