One of these claims which, in my uneducated opinion, is more than demonstrably false is Young-Earth Creationism (YEC). I don't mean to offend anyone who may believe in Young-Earth Creationism, but to my mind, I can't imagine why He would do that.
To create the Earth in one week, 6,000 years ago, would require pretty significant, and frequent, violations of known laws of physics. If He could accelerate the Creation process in such a way, then why did it take a week? If He is capable of performing such huge violations of the laws of physics, then why not just snap your fingers and have it all be there? I don't know that there is a coherent answer.
In addition, if He did create it in one week, 6,000 years ago, then why would He also create huge amounts of physical evidence that it took much longer? Literally everything in the universe, from coral and tree rings, to the time it takes starlight to reach us, testifies that the universe has been here for much more than 6,000 years.
The more insightful among you may say that He did that in order to mask his presence, such as in an old refutation to the Argument from Non-Belief. He needs only those who are prepared to know of His existence in order to protect the unprepared. But that doesn't quite fit. No matter how God created the Earth, He could have masked His existence. Old-Earth Creationism doesn't bring us any further to proving his existence. In fact, wouldn't Old-Earth Creationism be the more reasonable model, if He were trying to hide His influence, since it looks much more like the natural process?
A bigger problem is that if God did leave such evidence as fossils and such in order to throw us off, it would be closer to deception than masking his existence. In other words, it would not simply be the absence of positive evidence, it would be the presentation of negative evidence. God would be telling a lie, rather than simply not saying anything at all, and according to Christian canon, God cannot lie.
In other words, no matter how you choose to interpret the first few chapters of Genesis, it difficult to see Young-Earth Creationism as not conflicting with the rest of the Bible and how we conceive of God, in addition to simply leaving many, many questions unanswered, and contradicting the many signs to the contrary.