If I am not mistaken the regular birch ply you find in places like the BORG are graded the same as other domestic plywoods. Baltic birch ply on the other hand is imported on GOST(???) standards. Here is a description I found for the grading of Baltic birch ply.
Grade B-Select one-piece face veneer is generally light and even in color. Some small, closed pin knots may be allowed, as well as some brown streaks. NO patches or voids are allowed. The surface is well sanded.
Grade BB-One-piece face veneer is generally light and uniform in color. Occasional pin knots and mineral streaking is allowed. ALL open knots and defects other that those allowed in grade B have been cut out and replaced with oval patches. The patch veneer is the same grade and specie, and is typically of the same color. The surface is sanded.
Grade C-This grade allows patches, open knots, and veneer splits. Grade C is not normally sanded.
So I guess the B-BB Baltic birch you were asking about would have one face graded at B and the opposite face graded at BB.
I hope this helps and if I am off base I am sure someone more familiar with the grading can correct me.
Any plywood is OK to paint. It depends on what you want the plywood for. If you bought a furniture grade plywood that had a mahogany veneer you would probably want to stain it or apply a clear finish. Baltic Birch is usally a better grade of plywood it has more plys to it. There are usally no voids in the board. People use it to make fixtures or furniture. You can even get it with a phanolic finish. Any grade of baltic birch would be good to paint the grade of the plywood should be determined by what you intend to use it for.
Thanks Alan. I am building "built-ins" for the wife. It is actually a neat project: open lockers for the kids to throw their stuff in when they come into the house. I plan to have a little bench seat at the botton of each looker that opens up for shoes. Their will be 4 lockers about 18" wide to hang coats, book bags, etc. The house trim is a glossy white paint so I wanted to paint it to match.
Now the only trick will be to train the kids to use them. :eusa_pray