Please don't take this the wrong way, but I think you're putting the cart before the horse. Before you can be successful at selling hatching eggs, you must have a market. To create the market you must have had good birds of a given breed for some time. Ideally, you show your birds, and do well at shows, so that people know your birds are worth buying eggs from.
As to what breed, well, you need to get a breed that you really like. One you personally are happy with. One you want to work with, and show. Then once you've built up your reputation as someone who knows what they have and does a good job breeding it, then you might think about selling hatching eggs.
And fwiw, I don't think anyone gets rich selling hatching eggs...