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Can you help me come up with toy field theories to practice calculating cross-sections? I'm not considering theories with derivative couplings like scalar electrodynamics.

The interaction vertices I'm aware of are [itex]\bar{\psi} \gamma^\mu A_\mu \psi[/itex] (QED), [itex]\bar{\psi}\psi\varphi[/itex] (Yukawa), [itex]\bar{\psi}\gamma_5 \psi \varphi[/itex] (pseudoscalar theory), [itex]\bar{\psi}\gamma^\mu B_\mu \gamma_5 \psi[/itex] (axial vector), [itex]\bar{\psi}\psi\varphi^2[/itex] (don't know if this has a name). What are some other creative field theory interactions?