What should a rational responder look into if they want to be able to respond rationally? The simple answer is everything, but no one person can know all so we should probably narrow down a few points. I think the way we should go about this is by having basics and give a starting point. Most of this will center around an atheist view point and this is something that should have input from others, mainly when it comes to specific areas.
A. Logic: This is the most basic foundation for finding knowledge and evaluation ideas.
B. God Arguments: There are many(300+), but you need to know a few common ones and how to break them down.
1. Pascal's Wager
2. First Cause/Unmoved Mover/Cosmological Argument
3. Grand Design/Argument of Complexity
4. Argument of Possibility and Necessity
5. Anselm's Ontological Argument
Here is a nice list with a few more with responses.
C. Response Arguments: This would basically be arguments with the idea that we should shut up, know them and how to respond.
1. You can't criticize faith.
2. You should be tolerant.
3. Religion doesn't harm.
4. Argument from Relativism/There is no answer.
5. You are no better thing the fundies.
D. Science: Degree or not you will need to know some things about science.
E. Historical: There are elements in history that should be known.
1. History of Religions
2. History of Governments
3. General History
F. Text: Basically a reading list of good info or books that may be referenced.
1. Bible: If you deal with Christians it will come up.
2. Qur'an: In the US probably won't come up as much, but it might.
3. The End of Faith by Sam Harris
4. The God Delusion by Richard Dawkins
5. Breaking the Spell by Daniel C. Dennett