I was adopted at 6 weeks old and would like to give some perspective.
My parents were advised in the 70s to introduce us as "their adopted chidren". This was standard advice back then and in fact among my adoption papers was a leaflet telling parents to do just that.
I think the authors had not spoken to any adopted children.
I clearly remember being aged 3 and the sick feeling in my stomach as I was once again introduced as "our adopted daughter"... It made me feel second best. Not quite as good as a bio child.
The problem is that when your introduce your child as being adopted people start asking questions while the child stands there listening absorbing the info and attitudes.
This was 40 years ago but those conversations stayed in my mind.
"does she know who her real parents are"
"Is she a bastard?"
"Is her brother x her real brother"
Another reaction is people telling the adoptive parents "how wonderful they are" for adopting. As an adopted child it made me feel that I must be pretty terrible if my parents had to be congratulated for taking me on!!!! Once again terrible for the self esteem :((
Another thing to bear in mind is that birthdays can be an incredibly painful day for adopted kids. I would feel as if a dark cloud had descended on me in the days before my birthday. Inevitably on that day I would be sad knowing even as a young child that my bio mother would be thinking of me. I would normally self sabotage my birthday parties.....I did not want to celebrate a painful day but could not express those feelings at a young age. It was hard to laugh, eat jelly and ice cream and pretend to have fun when I was sad. I would suggest keeping actual birthdays lower key and maybe having the party a week or so later.
My parents never discussed our adoptions or the day they received us. The subject was and still is taboo. My adoptive mom died when I was a teen ... On her death bed she asked me to promise to not search for my bio family!!!!
I did search for them years later but feel terrible guilt about that and know my dad was against the search. I have cut off contact with my bio parents due to the guilt. Please don't ever put your kids in that position.
Also please think carefully how you handle the subject of trying to conceive pre adoption. My mom used to say "we were so sad we could not have children of our own and then we decided to adopt"!!!! I once again felt very second best.
Just typing those words has reduced me now to a flood of tears.
Having said all that I could not love my dad more if he was my biological dad. He has been the most incredible father and grandfather and I have been blessed to be his daughter.
The fact you are here asking for advice tells me your children are going to be very loved too.
Love and an acknowledgement of the pain your children will carry with them are the best 2 things you can give them.