Note: I'm not a modeler myself, but tested several recipes of rocket candy and read rocket modeler forum for a while.
First of all, you have to think if you will be satisfied with solid propellant or want a liquid fuel engine.
Building home-made liquid fuel rocket engine is very hard. One need to find pumps, make combustion chamber from something very heat-proof and reasonably stable chemically. Anyway, some successful reports may be found on the internetz. Note, however, that if you can choose safe liquid fuel, like kerosene or some alcohol, there is no safe oxidant for liquid-fueled rocket engine. The closest thing to safe oxidant I can imagine is nitric acid, that require work on fresh air or in specially designed room and tends to form explosives on contact with many things, like milk protein (yep!), some of which are volatile
Solid-fuel model propellants are much easier to prepare and use, there are numerous articles in the internetz about such fuels. The most common one is rocket candy, prepared from potassium nitrate and sugar. I tried it to see how it works (I didn't build any rockets), but instead of sugar I used sorbitol. Rocket candy based on sorbitol can be melted and then can be casted in any form. wiki article contains both info and links to sites with well-testes recipes by successful modelers.
Another possible option is making missile model based on some classical jet. There is quite simple pulse jet and there are some books about home-made turbine jet designs.
Anyway, I recommend to search nearby rocket modeling club and find supervisor.