In general, things like temperament are very loosely correlated with breed. More depends on their environment. So, I wouldn't take any of this as a defining thing behind breed selection, only as an opinion based off my extremely small bird sets. Yes, there are some lines with distinct tendencies, but the overwhelming majority of birds are just chickens and make good backyard birds for most people. "The plural of anecdote is not data." 
Friendliest chicken: Naturally friendliest? An EE x Sultan mutt. I barely handled her as a pullet and she still climbs on my lap at every opportunity. 
Most skittish chicken: Currently a Dominique cock. This depends mostly on handling... I've never met a bird yet that I couldn't tame if I wanted to put the time in. I've had a bunch of other skittish birds but I can't recall breeds. I've had about 200 chickens so my memory isn't perfect on everything. Leghorns can be pretty jumpy if you don't raise them yourself.
Best layer: White Leghorn, far and away. I've been getting an egg a day from those lovelies through almost the entire winter.
Worst layer: Hmm, I'd say my Welsummer Olive Egger, a designer mutt type of breed. She hasn't given me over an egg a week since last summer. She's about two years old.
Largest egg: That's an age thing, but my sexlinks gave me the most consistently largest. They couldn't fit in the cartons. 
Smallest egg: OEGBs, but no surprise there.
Prettiest egg: Shell colour? My Ameraucanas lay a nice blue, and the above mentioned olive egger has pretty eggs when she gets around to presenting me one. I don't own any breeds that lay a dark brown egg. Cayuga ducks lay neat black eggs for the first part of their laying cycle.
Top of pecking order: I don't know. I seem to have more of a rotating pecking order. Perhaps because I have a steady stream of birds going in and out of the flock. 
Bottom of pecking order: Again, I don't know. Perhaps the EE x Sultan mentioned in the first question.
Smallest chicken: OEGB. I think one of my hens clocks in at about a pound and a half. Can't go smaller without sacrificing cold tolerance.
Largest chicken: Partridge Chantecler or Australorp.
Favorite chicken: Breed? Partridge Chantecler, for their colour, productivity, cold hardiness, size, docility; Silver Ameraucana, for their plumage and egg colours, hardiness, and body type; and White Leghorns, for their incredible rate of lay, feed to egg conversion, cold hardiness, range wariness, and intelligence. I'd highly recommend White Leghorns for a free-range backyard flock focused on egg production in a more southern climate, i.e. anywhere south of Toronto without temperatures much below -10F. in winter Even the hens get frostbite when temperatures are below zero F for weeks on end, which is their flaw. They're cold hardy in all other respects, though, and not prone at all to falling over dead because the winters are 'too much'. I've only owned about 10 so far, though. Favourite individual? Spangled OEGB, a spoilt rotten 3-year-old hen.
Least favorite chicken: Sexlinks. Can't stand them. They have Leghorn-like personalities only on overdrive, they eat a lot, they die young. Plus they're plain in colour. Would not recommend unless you're looking to keep birds for one to two years only and buy replacements from a feed store instead of breeding. They were created for a specific purpose, and if that happens to be the purpose you want them for, fine—that's just not what my flock goal is. I've tried about 20 different breeds—more if you count mixes or varieties—and they all had their flaws, or reasons they didn't fit my flock. I found what I wanted in the PCs and Silver AMs.
As a note I hear some of the same complaints about Leghorns, the hatchery White variety in particular. They are a bit on the pecky side of things but they haven't made me bleed like the red sexlinks have. Little cannibals, they are.
I have a flock of about 40 birds at the moment, counting ducks and quail. 10 Silver Ameraucanas, 5 Partridge Chanteclers, 5 quail, 9 ducks, 4 White Leghorns, 3 bantams, and a bunch of other breeds and mutts that I can't recall at the moment. I keep birds for eggs and breeding to the Standard of Perfection. Bug control is a plus. Their meat tastes fantastic but it's not a main reason I have them right now. Quail are pets, ducks are pets and eggs.