I like my crested Polish, honestly. If you get them from a hatchery, they lay just as frequent as other breeds. (At least mine do. I count on them every day)
I also free range mine, and with their blending colors in our pasture, they've never been picked off. In fact, I've lost two girls in the forest for 2 weeks and found them alive and unscathed.
Well you have what I think is the all time best white egg layer and that is Game Breeds like American Game and Standard Old English but you could also go with;
Leghorns --
Dark Brown
Light Brown
Buff
Black
Silver
Red
Black Tailed Red
Golden Duck-Wing
Minorcas --
Black
Buff
White Face Black Spanish
Blue Andalusians
Anconas
Buff Catalanas
Hamburgs --
Silver Spangled
Golden Spangled
Golden Penciled
Silver Penciled
Black
Small pretty chickens, smaller eggs the 1st season, but then regular size eggs.
Would rather free range than eat feed. But they can fly and are independent when in a flock of same.
Can handle the heat.
I adore my Golden Campines who are 3 months old or so. They haven't started laying yet obviously. They are flighty, meaning that they don't want to be held or caught. But they are friendly and come up to me to "smile" at me.
They are not too cold hardy. I have 19 of them.
They constantly go in and out of my large fenced garden- they really have to not be penned up in small quarters to be satisfied with life. They fly well.
I have been threw tons of birds trying to find the perfect white laying stock and to make a long story shortout of 7 breeds I have sold off every last flock but my Minorca's they clearly lay the best white eggs. There so crisp they crack right open. in my experience they win hands down. They even out layed my White leghorns which I were definatly unimpressed with. There to flighty of a birds skittish and agressive in large open flocks.
Minorca hands down...many of the other breeds mentioned don't lay that large of an egg..the Minorca will lay jumbo just as the white leghorn does and does lay as well as the white..my white lay 6-7 days a week jumbo by weight every day so I can't say outlay but they are awesome hens.