I too, have been sceptical on the Big Bang theory for a long time now. It's main problem is as Terrence McKenna so eloquently put it: "Give me one free miracle, and I can explain everything else for you." I think it's the terror of having to comprehend infinity that drives so many to look for a beginning and an end to the Universe. Probably the best documentary I've ever seen on the steady state universe is The Cosmology Quest
Infinity is terrifying, but at least we know no human will have to suffer that experience.
The steady state theory definitely has problems, but I do vastly prefer the theory in its neutral stance on existence.
Most of the "proof" for the big bang theory was already theorized to exist before it was used to prove the big bang theory. Some of the supposed "proof" actually disproved it and the theory was later changed to fit models. Take the example of the microwave background, one of the most common examples of 'proof' in the big bang theory. The big bang theory predicted a microwave background that was far more intense that what we actually found. The theory had to be changed to fit. Whereas, scientists had postulated the microwave background for a very long time in the steady state theory. The questioning essentially went: If there are stars everywhere in the sky, why doesn't space look like the surface of the sun? The natural and obvious answer to that question is that something about space must reduce the energy of light the further it travels. They then tried to calculate what this reduction of power was and then used it to infer the heat of the universe at the microwave spectrum. This prediction -exactly- matched the microwave background.
Because the political engine behind the big bang theory is so strong, ideas were created that could be used to explain this difference (Red shift due to stretching of space time) that can not be proven or dis proven without a vast undertaking of science that humanity is not capable of currently, and the theory was edited ad hoc to incorporate these ideas. In the final, most perverse part, it somehow became accepted generally in scientific history that these were events that proved the big bang theory.
To me the huge difference between good and bad science, is the steady state theory has a ton of ideas about what could be reducing the strength of light over time in space, but none of these theories are accepted into the bigger theory because none of them have been proven to any degree. The big bang theory will tell you why this is happening, and the theory is based around that explination of why even though it has no real scientific merit. This is the scientific process in reverse. Our understanding of nature should never be colored by things we don't know to try and make ourselves seem smarter than we are.
And as a little pre edit: Don't come in here waving around gravitational redshifting as proof of red shift. They are -completely- different beasts.