What you said sounds correct to me.
About 1/4 of the chicks should be black
About 1/4 of the chicks should be blue
About 1/4 of the chicks should have some kind of black-and-red pattern
About 1/4 of the chicks should have some kind of blue-and-red pattern
All of them should have white barring over top of those colors/patterns.
The "some kind of pattern" may resemble what a Cream Legbar has, or it may resemble what a Rhode Island Red has, or it it may have the colors arranged in some other way yet. It may also vary somewhat from one chicken to another.
The next generation may have more red bleeding through, and may also get some silver (white) bleeding through.
As
@Lady of McCamley said, this first generation all have one copy of the pea comb gene and one copy of the blue egg gene. What she didn't mention is that those two genes are linked: they are close together on one of the chromosomes, and are usually inherited together.
The way the linkage works:
pea comb can be linked to blue egg (Ameraucana)
pea comb can be linked to not-blue egg (Brahma, not in your project)
not-pea comb can be linked to blue egg (Cream Legbar)
not-pea comb can be linked to not-blue egg (Rhode Island Red)
You have three of those four options in your project
In the next generation, you can use that linkage to select chicks that should be pure for the blue egg gene.
About half of the chicks will have pea combs, and the other half will have single combs.
Most of the single comb chicks will have one copy of the blue egg gene (from the Cream Legbar), and one copy of the not-blue-egg gene (originally from the Rhode Island Red.)
Most of the pea comb chicks will have two copies of the blue egg gene (one from the Cream Legbar, and one that traces back to the Ameraucana.)
The genes stay linked most of the time (the literature says about 19 our of 20 times), so it's fairly accurate to pick them by comb type in that generation.
If you want to be entirely sure, there is now a DNA test for the blue egg gene:
https://orders.iqbirdtesting.com/product/blue-egg-gene-with-feathers-sample/
It can tell whether a chicken has one copy, two copies, or no copies of the blue egg gene.
Whether it is worth the money to test chickens for your project, I do not know.
Testing is probably cheaper than test mating, if you do decide you need to know. (Test mating requires breeding the chicken to one without the blue egg gene, raising up a bunch of daughters, and checking what color eggs they lay. That way you can tell how many copies of the blue egg gene are in the one being tested. But that takes months, and you use a lot of feed raising the pullets to egg-laying age.)
If you once get a flock established with all birds being pure for the blue egg gene, all of their offspring will breed true for it as well (unless you introduce the not-blue gene again.)
Do you know which kind of comb you want to end up with eventually? Since you're already working with Ameraucana and Legbar, you could go either way and still get blue eggers.
In later generations, if you cross back to not-blue-egg breeds, you might be able to plan matings that let you track the egg color genes by comb type, or you might not.
I expect the next generation to have some variation in size, and the generation after that to have more variation. Obviously, the way to select for larger birds is to breed from some of the biggest ones in each generation.