That coop has about enough space to house 6 standard or 12-ish bantam chickens assuming they never get out of the coop (and are relatively docile, you're not going to want 6 leghorns in there). If you DO plan on letting the chickens out for at least part of the day almost every day, you can squeeze more in.
Chicken math is best explained with examples, so... "We use about 2-3 eggs per day on average so we need maybe 4 or 5 hens" turns into "Surely that count is wrong, there simply cannot be 60 birds here" in a year.
Now for the chicken breeds... oh the choices! I'm going to join the chorus of "mixed flock" voices, I'm pretty convinced that most home flocks should start with a sampler set.
My suggestions, in order of how friendly/personable/cuddly I have found mine (every bird is an individual, and a lot depends on how they're socialized):
Silkies - they're adorable, non-intimidating even to people who are unsure about birds, super friendly, and they lay bigger eggs than seems reasonable for their size.
Brahmas - they're big, docile, and friendly. They're probably the easiest chickens I have to pick up and hold on to, they actually seem to like it.
Marans - I have black, black copper, and a cuckoo marans. They're laid back and personable, and lay nice dark brown eggs (the black copper marans lay the darkest cocoa-brown egg).
Speckled sussex - I can't speak to the other color varieties, but the speckled sussex achieve almost turkey-like levels of being underfoot and into everything you're doing. For whatever reason, their color pattern doesn't seem as impressive in photos as it does in person, too - they're absolutely gorgeous.
Australorps - Very good layers and while not as in-your-face friendly as the ones above, they're sweet.
Something that lays a blue/green egg, they're so interesting and a great thing to show around. Easter eggers are relatively easy to obtain but more hit-and-miss with their personality than most breeds - I have a couple sweethearts and at least one who's convinced I'm going to kill her and the entire flock any minute. My cream legbars are pretty even-tempered but not super cuddly.
I have HEARD that the naked necks are quite friendly also, but I really can't get past their looks to find out for myself.
You pegged the Speckled Sussex perfectly! We had one we named Prissy. She followed my husband everywhere. I can still see the two of them heading to the workshop. She would get on our lap and just sit there and watch the world go by.
Australorps are also good mothers. I am down to one and need to pick up some more. I think chicken math may kick in here!