Australorps hold (or at least held) the record - one hen laid 364 eggs in 365 days. I've never had sex links. My 3+year old lone leghorn still lays almost daily, probably 28 a month. If you just want eggs, probably leghorns are the way to go; it's mostly what commercials use. They are a little on the small side and don't eat as much as a Australorp, which is definitely a larger breed, a "dual purpose" breed, meaning it's also good for meat.
But Leghorns are flighty, will run from you. It is unusual to get one to be friendly and let you approach it. I don't really make pets of them but I want to be able to handle them when necessary, and the Leghorn hollers and flaps if I pick her up, even off the roost -- I can't get near her without a net, otherwise. I have 3 Australorps and they all seem to lay almost daily; it's hard to be sure because I have several breeds with similar egg colors, and I've never tried to figure out exactly who did what. (The Leghorn is my only white egg layer.) And Australorps are a lot easier to handle. My friendliest, the two Speckled Sussex, seem to lay pretty well, but I think the Australorp do better.
Here is a chart that gives tells many eggs per week you might expect, along with a lot of other good breed info:
http://www.ithaca.edu/staff/jhenderson/chooks/chooks.html
It says 4/week for both sussex and australorps, and 6/week for white leghorns (mine is a brown leghorn.)