Information is knowledge derived through experience, learning, instruction, etc.  It is a collection of facts and truth. Because information is a collection of truth, true information ultimately comes from God.  I am not trying to be too philosophical about what information is. But you must understand that all truth is God's truth.  Therefore, proper and accurate information is synonymous with truth.  But having proper information is useless if it cannot be logically applied to a discussion.  So, not only must we learned how to think critically, so as to expose erroneous assumptions and conclusions, but we must support our assertions with facts, with information.  Therefore, if you want to think well, you must also have sufficient knowledge with which to apply proper thinking principles.  Generally speaking, the more you know the better you can think.  This isn't a truth axiom, but it goes without saying that if you have incorrect information, your conclusions may very well be inaccurate.
     You will find that as you learn in both areas, logic and knowledge, each will feed off the other and you will reach a threshold where breakthroughs will come more easily.  Breakthroughs are those times when you realize the truth you had not known before and/or those times when you were discussing something with someone and you even surprise yourself with what you say.  In other words, sometimes you put things together in a way that helps you learn even after speaking.
     Critical thinking requires experience.  Experience brings information. Experience is based upon what you do.  You remember what ihave done, where you have succeeded, where you have failed, and so you're increased experience brings information and, hopefully, wisdom.
     Facts are incredibly important when trying to win an argument, expose error, and establish the truth of the word of God. For example, someone might argue that the Bible has been translated so many times that it's not trustworthy. As far as critical thinking goes, I would first asked if that premise is correct. Has the Bible been translated many many times?  Also, what does the critic mean by "translated so many times"? Does the person mean that it has been translated from one language to another language to another language and finally into our language and that such multiple progressions inevitably lead to loss of meaning and that such loss, invalidates the truth of God's Word?  That is usually what people mean when they say that the Bible has been translated so many times it can't be trusted.  Of course, that is not truth because God's Word is not translated from one language to another into another, etc.  God's Word is translated directly from the original documents into our present language.
     When we know that the Bible is not repeatedly translated from one language to another language, finally arriving at ours, but that it is translated correctly from the original languages (Hebrew for the Old Testament and Greek for the New Testament), into the English, then we can not only ask the right questions to the one who is making this assertion, but we and also offer a factual correction. In so doing, the objection is removed by providing accurate information.
     Therefore, you need information, you need to have the facts in order to debate properly and establish the truth of God's Word. You cannot think critically without information and you cannot use information properly if you cannot think critically. Whether or not you are enrolled in the CARM schools of Christian theology and Christian apologetics, you still need to know the facts (those schools are full of facts as is the CARM web site). The more you know the better you will be able to defend the faith, expose error, and establish the truth of God's Word.