How to start the conversation which will lead to my coming out as an atheist?

It seems your mom would be more affected than your dad. Maybe you could take your mom out somewhere, like to a restaurant, and tell her there? This way she knows you mean business and it isn't one of those things you're just saying to get her goat. Talk about it in a mature manner, perhaps start out by mentioning the upcoming confirmation and then move on to say how it doesn't apply to your life.