Off the top of my head, for C I remember the following:
- stdio.h
- stdlib.h
- malloc.h
- string.h
- ctype.h
- limits.h
The most important ones for basic things are stdio.h, stdlib.h, and string.h.
FILE is just a struct of some sort. Types like size_t are usually typedefs to something like long int's on 32-bit systems and long long int's on 64-bit systems. Use those types where appropriate since you can't be sure they are compatible with other built in types if you want to be portable for both 32-bit and 64-bit systems.