I grew up with Moyen / Klein poodles (about 35-45 cm at the withers, a size category between miniature and standards, common in Europe but not recognised in the UK), and have a standard now. I find my standard more balanced compared to the Moyens, a gentleman not a child, but it may be down to his personality rather than generic size. I think smaller dogs tend to be more neurotic and yappy but it is a subjective view of course. All poodles are incredibly intelligent and emotionally intelligent, sensitive, playful and adaptable - equally happy to go on long walks or spend a day sleeping under my desk while I work. Importantly for me, hypoallergenic. Amazing breed, we briefly considered viszlas and Weimaraners but whilst very beautiful and athletic I don't think they make as good a family dog as a poodle.
In terms of costs and effort, yes standards need more food and take longer to brush /wash / trim. Mine is a Covid puppy so I started grooming him myself, in a proper poodle cut, having done it with my moyens before. I am pretty good with it but it takes forever and washing him kills my back. It is recommended that we trim the face, feet and tail (bottom) weekly but I just don't have time for it, he is lucky if he gets brushed weekly.
I paused when you mentioned the age of your kids. I dreamt about a dog for years and got one when my youngest was 4, and in the first year I still felt that it might have been too early. He adores the kids and treats the younger one as his favourite deity, but poodles are mouthy and sometimes when they play he can inadvertently scratch her with his teeth. Not sure if a miniature poodle is a better fit with kids - if a dog is tiny kids will just pick it up snd carry around, and can easily drop and hurt it.
Anyway, an excellent choice of a breed, I am sure whomever you choose will become a delightful family member very quickly!