Heat oil over medium heat in a large dutch oven. Add the cut sausage and chicken meat and fry until lightly seared, about 5 minutes.
Add the onion, bell peppers, and celery and cook until the onion is soft.
Add the garlic and cook for 1 minute.
Add the tomatoes, paprika, salt, cumin, oregano, basil, thyme, pepper, and cayenne pepper, stir well.
Stir in the white rice and chicken broth.
Bring the mixture to a boil. Then reduce the heat to medium low, cover, and allow to simmer until the rice is just cooked (about 20 minutes), stirring every few minutes.
Stir in the shrimp.
Cover again, and allow to simmer for another 5 minutes, or until the shrimp are cooked (depending on the size of your shrimp).
Notes
You can use all three meats or any that you choose.
Andouille can be substituted, see my suggestions above.
You can use your favorite cajun seasoning instead of all the spices.
This can be frozen, see my tips on how to do that.