Computations of Feynman diagrams factorize in three parts in general:
- The denominator has the same structure, regardless if you are dealing with scalar, spinor or vector fields.
- The numerator is different, you need trace identities for gamma matrices and so on, but can be calculated independently.
- There is a group theory factor, if you are dealing with a non-abelian gauge theory.
Because of 1., you can learn almost all the necessary tools for calculations from the case of a scalar theory. Since 2. and 3. introduce additional complications, they can be treated separately.
Conceptually all the different (free) fields arise as different irreducible representations of the Poincare group, in particular translations are generated by an Operator $P_\mu$, whose square is invariant $P^2 = M^2$. So even the components of spinors, for example, satisfy a version of the scalar Klein-Gordon equation, which is the reason for 1. above.