"I Believe" -- two very simple, common words with an uncommon amount of slipperiness. What is it to believe? What can I believe? What forms a belief?
To start, I believe that a belief is simply something that you're convinced is true. I use the word "convinced" very carefully. Beliefs don't have to be proven true. You don't need absolute knowledge of truth in order to believe something. I am convinced of the truth of many things, but there are only a few things that I absolutely know are true.
I know I think, therefore I know I am. I'm perfectly willing to put Descartes before the horse (sorry) and everything else on this. I find nothing useful about any definition of existence that allows thinking to exist without a thinker. I not only think, I perceive myself thinking. Of these things I am absolutely certain. They are foundational postulates, self-evident and requiring no proof. Everything else is, ultimately, a mystery. Does what I perceive exist independently of my perception? Is the continuity and consistency of my perceptions simply an artifact of my perceptual mechanisms? I don't know and can never be absolutely sure.
Unfortunately, there's no way for me to prove these few things I know to anyone else. If other people actually exist, I expect that they are stuck in the same philosophical boat as I am. They cannot have absolute knowledge that I exist. I cannot have absolute knowledge that they exist. Therefore, nothing we present to each other's perceptions can be taken as proof of anything.
Obviously, I have just completely undermined any further position I present, but let's turn to the practical outcome of what has been said. Whether the universe exists or not, I appear to have little choice but to treat it as if it exists. It is clear that I exert only minimal control over the content of my perception, indicating that I am only a component of reality, not its definer. It seems to follow from there that "I" am distinct from "not-I", that "not-I" has no dependence on "I" for its existence. I am convinced (or, I believe) this is true. But, it still leaves things a little short. What we have so far has been a reaction to reality. I need to formulate a larger set of beliefs to govern my interactions with reality.
In (cogito ergo) sum, then: I exist, I perceive, I believe. But believe in what?