My background is in music and linguistics, so here is my take.
My experience and studies confirm is that for the kids, it is all “words” at first, just the building blocks of communication. After a short time, they notice that certain people (grandma) don’t understand certain “flavor” words, and they use only that flavor word with grandma, and others with other people. They begin to notice that an object has several names (this is true in any one language as well) and certain people around them use some names and others use a different one. Pretty soon they are not only differentiating which words (language) they use with what people, they step in and begin to translate (for grandma).
So far so good. Here is the rub, and it is reading and general language acquisition. Remember, up to this point they are learning almost twice as many vocabulary words as most kids do, but there is some confusion between languages. They may learn one or two alphabets or at least alternative pronunciations of the alphabets. We now have 4 different communication systems, two oral, two written, all cross talking in their young brains. This is when most parents panic and decide on one language. The kids also have figured out which language is most widely spoken and understood and that becomes their primary language (For my kids it was English, foregoing their native Portuguese because we lived in the US, and all the media, grandparents, friends etc. spoke English.)
Here is the crucial part. THEY WILL BE FINE. It will take a little longer, they will have confusion, but by age 7 or so they will not get mixed up any more and will be bilingual and will catch up and surpass the other kids in language skills.
This is the crossroads where parents who wish their children to be ACTIVELY bilingual must INSIST they SPEAK (not just listen passively and understand) the subordinate or less common language (in our case Portuguese) at home. Otherwise they (brilliantly) figure out the easiest way to communicate is in one language since most or all understand that language. In our case our kids heard and understood our Portuguese, but answered in English. Only constant insistence, and withholding food and other privileges (it was mom who held all the power and wanted her native tongue not to die in our home) brought them around to become a habit in the home to speak Portuguese. They would ask her to pass the milk and she would make them repeat it in Portuguese before she would let them drink. Sounds cruel in writing but it was more a pain in the butt for mom, and a grudging gesture of solidarity to mom for them. It was just a gentle but constant nudge to get them back into the habit of SPEAKING their native tongue and keeping it active. As they grew older (now 13 and 9) they had visits from cousins, and visited Brazil and could speak with their family, and even interpret for their American cousin who came to Brazil with them. Their English was fine, no accent though their native language was Portuguese, but they have a weaker vocabulary and slight American accent (from their father) in Portuguese, which amuses their cousins.
They are not only bilingual, they are bi-cultural, and have great Brazilian social gifts and creativity with American focus and discipline, none of which they appreciate but we as parents marvel and envy them, as we struggled much later to learn our other languages, and know the gift we gave them to NOT think either point of view was the center of the world and the “only” truth.
Finally, to answer your question, which language should they read first? The one they will study with at school. Once they read one language the other is just a variation on a theme. In our case, our daughter began to figure out comic books in Portuguese without us teaching her, then we helped her, but this is also because Portuguese spelling and pronunciation is much simpler and consistent with the spoken word. English is notoriously inconsistent, but of course not as difficult as Chinese or Japanese in its written form, so they lucked out. If the choices were Chinese and English, I would really think you would have to focus on both very hard, though English gets so much easier after the first couple of years, Chinese and Japanese only get more intense and confusing the more combinations you have. They estimate it takes a Japanese child until the age of twelve to have the reading vocabulary of an 8 year hold English reader. But all this grows their brains and builds a double platform that will allow them to live, dream and think in completely different modes with equal fluency. The human mind is amazing. I commend you on wanting to give them the gift of multiple languages and keeping them connected to more of the world and their extended families.
My son teases his cousins when they mock his weaker Portuguese or doesn’t understand them at first. He simply says (in Portuguese) “Can you say that one more time, S-L-O-W-L-Y and in ENGLISH?” In other words, stop busting my chops, I am speaking two languages here. The cousins are now studying English as well, and it is one big extended happy family.