There are several different breeds that could meet your needs. What you will get a lot of on this forum is personal preference. As long as you stick to some of the basics, it is hard to go wrong with any of them.
Easter eggers are not a breed, but a type. They can be about anything as long as they might have the blue egg gene and might lay green or blue eggs. They are probably a pretty good choice for you. Some others I would mention are Sussex, Rocks, Delaware, and Australorp. There are plenty of others, but these would be my preference. I'd tend to stay away from the ones that are known to go broody a lot, although any of these may go broody.
A strong one for you to consider are the sex links, either red or black sex links. These are not breeds but are specific crosses that can be sexed by color or pattern at hatch so you are sure of getting females. You sound like you don't want any roosters. They go by a lot of different names, but if you see one with "star" in the name, it is probably a sex link.
As far as how many, I'd suggest a mimimum of three. Chickens are social animals and really need to have other chickens around. If you get three and something happens to one, they still have some company. During laying season three hens of these breeds will probably give you around 15 to 18 eggs a week, maybe more and maybe less.
Good luck!