What you describe is more like Deism or Theism, where you believe in some sort of higher order intelligence behind the universe, but it's not incompatible with science and rationality and observation. You can't believe in both Creationism and evolution because Creationism is an explicit denial of evolution, and of anything but a literal reading of Genesis. But you're in good company, as you just described many/most of America's Founding Fathers, who today's Evangelicals would have lynched as heretics if they bothered to read their actual words rather than treat them as cartoon mascots for whatever they want to imagine America stands for at the moment.
And why do all the creatures (you claim were created out of thin air) as if they had common ancestors? Both physiologically as well as genetically?
To quote Dobzhansky: Nothing in Biology Makes Sense Except in the Light of Evolution.
Why Evolution is True by Jerry Coyne might help you resolving that last part of the puzzle.
My vision is one I grew after reading several texts of several sources and reflecting about them, not only traditional religious texts but more esoteric and occult texts about it. It's very interesting to see that they mostly complement one another. If you get an esoteric hermetic text or something about how creation occurred you see that it doesn't negate the Bible, and it doesn't negate Science at all. It just goes deeper and deeper, mostly using symbolism.