Finally, on rationality, and arguments for the existence of God, is the intelligibility of the universe. Nature is known as God's second book. The fine tuning, the design, the rigid order and predictableness ('uniformity') in nature. You may have understood the concept of 'rationality' as that pertaining to the framework of the scientific method, anything deducted outside of which is 'not rational.' If this is the case, please look into why you're mistaken about this conception of rationality also and realise your error. In summary, though, the scientific method, as I'm sure you're aware, is about making hypotheses from the observabale natural world that, ideally, we can verify through repreated testing to observe results and affirm a conclusive theory. Because it is limited to observable phenomona, the scientific method is limited to making statements about the observable (natural) world. Therefore the scientific method cannot make conclusive statements or theories about pheonomona that lie outside the observable natural world i.e. the supernatural including God. As we've already seen in pic in we can be perfectly rational using philosophical and purely logical methods which do not invoke the scientific method. People who believe that the scientific method is the only legitimate way of obtaining truth about the word subscribe to a philosophy (often unknowingly) called scientism. Because God is transcendant (as well as immiment) the scientific method by default cannot and should not be looking for God himself as an entity in the natural world. Having said this, to theists who are already aware of the existence of God, the beauty, complexity and vastness of the natural world spell G-O-D was here as crystal clear as winnie the pooh day. Hence again a) is why nature has been described by some as God's second book and b) again simply from the observation of our universe and experience of our existience, God's own existence is literally screaming out at us all. Another thing to note is that in terms of the philosophy of science, it is generally accepted that the scientific method cannot make definitive claims about what is true. Many people do not understand this and operate on the 'scientismist's' assumption that the scientific method is actually the only way to validly invoke a truth claim. Nevertheless, contrary to what the scientismist says, the best is can actually do is 'we haven't falsified this theory…yet. ' So again just another bit of food for thought if you were coming from this relating your concern for 'throwing rationality out the window if coming to Christ' or however you phrased it..the rationality of the scientific method is not all encompassing…AND YET..if it weren't for God's order in creation, his design, his infusing of uniformity into our natural world..we wouldn't even be able to develop the scientific method!! (And exist as we do also, lol but besides the point). Our reason is God-given, and there is none apart from him.
My how I've babbled, and haven't even mentioned the other two tiers yet. Essentially though, look into the arguments for God's existence. There are a number of philosophical ones (as per Aquinas above, Ontological is another one) and scientific ones (teleological and kalaam cosmological). Then there's the moral argument which was crucial in my coming to all this and the conclusions of the argument made acknowledging his existence an absolute necessity as a means to avoid inevitable insanity/life-long dispair/suicide. But it may not be such a biggie for you.
The other two tier bits should be a bit shorter and incoming shortly..