For a blue egg, you can only get it by crossing blue x blue or blue x white. Crossing out to brown will give you green, and you can't go back until you've crossed to a blue again, and possibly again after that. (in terms of a true blue, not a robin's blue or a teal blue)
White with brown smudging here, crossed to a barred rooster, will give 50% barred birds and 50% white birds with very faint barring.