Heat a large skillet over medium-high heat. When hot, add 2 teaspoons of oil and swirl to coat. Add half of the chicken and sausage; cook and stir until browned on all sides, but not cooked through. Transfer to 6-quart slow cooker; repeat with remaining chicken and sausage. (Add more oil if needed for the second batch).
Return skillet to stove over medium-high heat. When hot, add 2 teaspoons of oil along with garlic, onion, celery and bell pepper. Cook and stir, scraping up any browned bits until vegetables are softened. Transfer to chicken and sausage mixture in slow cooker.
To mixture in slow cooker add tomatoes, Creole seasoning, smoked paprika, and salt. Stir mixture to combine and set slow cooker to High; cook for 4 hours.
In the last 15 minutes of cooking, stir in shrimp. Once shrimp is cooked through stir in hot cooked rice. Season to taste with salt, pepper and hot pepper sauce or cayenne pepper. Serve.
If you don't like chicken thighs, you can substitute boneless, skinless chicken breasts, but they won't be as juicy.
I've used both Creole and Cajun seasoning blends for this and either work well. Cajun seasoning tends to be spicier and Creole seasoning more herbaceous.
Note that you'll want hot cooked rice ready when the meat mixture in the slow cooker is finished cooking. I like to use long grain, brown rice, but white rice is also great.