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Actually, rocket propellants have long been made from very common ingredients.
And, in theory, you could really make them from scratch, even today, collecting and processing barnyard ... into nitrates ... but let's not go there. It's easier to find KNO3 (potassium nitrate, the main ingredient in black powder) at a well-stocked nursery, garden, or agricultural supply. We see it frequently here on eBay.
The Chinese were making rockets from natural saltpeter, charcoal, and sulfur packed in bamboo tubes more than a thousand years ago. When I was a lad, saltpeter was sold in little squat 4-ounce glass bottles in every drug store, for about a dollar-and-a-half. The sulfur was a shelf or two away. Not so today, at least in my part of the world, but as far as I know, these ingredients remain freely and legally bought and sold. In fact, they're usually offered here on eBay.
Dr. Robert H. Goddard, who invented the first liquid-propellant rocket engine, worked for decades with black powder propellants. Later he used liquid oxygen and gasoline to power almost all of his successful rockets. In the United States, most well-stocked gun stores have black powder in various granulations, as well as the alternative "Pyrodex" powders. (America has permitted Americans to buy and use black powder since the 1700s. It's up to $20 or $25 a pound now, but the quality is excellent.)
Liquid oxygen is a common industrial product, available in almost every metropolis. "Bring your own Dewar flask, please" may be the case, but the per-liter price is not extreme. And liquid oxygen remains the most powerful oxidizer around, and works well with almost any liquid hydrocarbon fuel, from alcohol to xylenes.
If you're keen to teach yourself powder making, you'll need to find some good quality potassium nitrate, some charcoal, and some sulfur. The nitrate and sulfur are widely used in gardening and agriculture. They're not expensive. Willow charcoal works better than bar-b-que briquettes, but charcoal isn't usually difficult to find or make. To do it right you'll need a ball mill, milling media, a safe and legal site, and the correct how-to information before you start. If you're experimenting with small motors, consider buying ready-made black powder at your local gunsmith shop.
NO, do not use--do not think of using--any kind of "gunpowder" or "smokeless powder" in any of your rockets. It will not work, and it will produce disaster more often than not. Black powder can be processed to work, but nitrocellulose-type (single- or double-base) propellants will NOT work!
If you want or need more energetic chemicals, you'll probably need to find a pyrotechnic supply company (there are two or three large ones in America). The pyrotechnic suppliers offer perchlorates, finely powdered metals, and other useful propellant products. The same suppliers will advise you about what regulations and laws to follow.
Before seriously considering any rocket propellants, why not read all you can from two or three good (accurate, up-to-date, complete) textbooks on the subject. We can recommend several to look for:
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