The Ontological argument would be that by the use of reason and intuition, if man can think of or conceive God, then God must exist. The Teleological argument would be that there is agreed upon evidence that everything in nature has a purpose or reason for being. This being true, then God has to exist by reason that God created all of this and gave it purpose. The Cosmological argument would be that everything is created with for a reason and the God gave everything that reason. I think Cosmological and Teleological arguments are similar in this way of thinking.
The philosopher I believe made the strongest impact on me would be Leibniz and the Cosmological argument. Our lives and existence on this planet our so complicated, yet everything seems to fit together and serve a purpose. I know that things happen in the world and we wonder what purpose did that serve, why did that have to happen. In the end, if we really look at the event objectively and without emotion, we can find the reason. I think of just one thing, the human body, and I have to marvel in its design. How could someone come up with the idea and design which allows our bodies to function?
We are, in essence a perpetual motion machine. Our systems are more complicated then any other piece of machinery out there and even with all of our advancements in computers, not one can compete with the human brain. They are amazing, yet they are only as smart as the person who programmed it. Yes, some of them are able to learn but this is only because the programmer has taught them to do so. This is just one aspect of life. You do not have to believe in God per say, but you can not go outside and look around you and not believe that there has to be something out there.