I was surprised to read that Redstone used 75% ethyl alcohol as a fuel. Looks like this idea was abandoned later, and modern rockets use rectified petroleum or liquid hydrogen instead for burning with LOX. I think it would be really strange for somebody to think about the alcohol before trying the usual jet fuel, kerosene, first. For which reasons the alcohol has been initially selected?
The Redstone's engine was based heavily on the engine of the German V-2, which also used 75% ethyl alcohol fuel with liquid oxygen.
Robert Goddard's first liquid fueled rocket experiments used gasoline with liquid oxygen, which burned extremely hot -- Goddard burned out several nozzles and combustion chambers on his early flights. Figuring out how to cool down the combustion chamber and nozzle became the big barrier to developing more powerful engines.
One route was regenerative cooling: running the fuel through tubes around the engine and nozzle to pull heat before spraying the fuel into the combustion chamber. This was complex, and when jet-grade kerosene (which is made of a mix of different hydrocarbons) was used, some of the fuel would vaporize, making gas bubbles that didn't carry much heat, and some of the fuel would polymerize or "coke", clogging the cooling tubes. Ethyl alcohol, on the other hand, would vaporize but not coke, and diluting it with water kept the temperatures down enough that vaporization in the cooling tubes wasn't an insurmountable problem. The water absorbed a great deal of heat in the combustion chamber and was expelled as steam, providing reaction mass to produce thrust, without contributing to combustion.
As a side note, Bacardi 151 or similar high-proof liquor is, essentially, 75% ethyl alcohol, 25% water. If you've ever had a flambé shot or dessert, that's basically Redstone rocket fuel -- but burning it with LOX (a little denser than water) instead of atmospheric oxygen (only about 20% of the air around us) makes for a much hotter and faster burn.