Leghorns set the record for most eggs laid Ina year and they lay large -extra large eggs. The downside to leghorns is that they are flighty. They are also not very cold hardy because they were developed in Italy. I would say a friendly cold hardy layer would be a wyondotte.
Yes, the record was set by a White Leghorn in 1979 (371 eggs in 365 days). Until that time the record was held by a Black Australorp (364 eggs in 365 days in 1924), although among brown egg layers, Black and Red Sex Links are the hens that most consistently exceed 300 eggs per hen per year.