True jambalaya will have pork sausage but chorizo is the wrong ethnicity and would toss off the spices. Smoked Cajun-style sausage might be mistaken for chorizo visually but the spice balance in the ground-up content would be different. Ideally, jambalaya would only have pork sausage or deer sausage, but pork meat chunks (like ham cubes used for cooking seasoning) are not uncommon. Beef sausage would work but would not be "authentic."
As to spices: Paprika is a middle-European or eastern European spice and is a very mild pepper on the (logarithmic) Scoville scale, sitting in the 50-100 range. We almost never use that. True Cajun dishes, if meant to be peppery, would use ground up cayenne pepper, which is in the 50,000 range. The compromise is Tabasco sauce, which is rated at 3500-3750 on that scale.
For comparison, the pepper spray used by police has been rated at 5,300,000. Pure extract of capsaicin is 16,000,000, and there are a couple of chemical extracts from certain naturally growing Moroccan sponges that are in the 15,000,000,000 range. The extract is resiniferatoxin and you just know that anything with "toxin" as part of its name will NOT be pleasant.
Cajun and Creole cooking will be characterized by base content as well as spice mix. To be honest, Cajun and Creole, though having different origins, are related by a certain commonality. They are based on things local to the areas in question. Cajun cuisine is limited to the bayou country of south Louisiana (in origin) while Creole cuisine comes from both wetland AND non-wetland origins.
True Cajun cooking will use the creatures found in the Louisiana wetlands, which includes wild boar, goat, deer, duck, chicken, fish, shellfish, crustaceans (such as shrimp or crawfish a.k.a. crayfish, French ecrivisse), and less likely things such as "alligator gar" (a type of fish like a barracuda), nutria (a.k.a. coypu, a very large South American member of rodentiae), alligator, turtle, and maybe a few other critters. Nutria is NOT native to the area but was introduced to control vegetation. It has been adopted as a gamy but edible meat source, kind of like rabbit and racoon. Beef, however, is not on the Cajun menu that often because in the wetlands, cattle tend to sink into the mud and drown. Since Creole cuisine is not limited to wetland origins, some beef dishes MAY show up in recipe books, but the cattle kept in this area were mostly for dairy production.
Creole and Cajun have in common this fact: The recipes originated in a time when refrigeration was not common. You couldn't afford to ship ice to south Louisiana and the compressor-based cooling devices were few and far between. SO ... you could tell how old your base food was by how much pepper had to be added to it to cover the fact that you were eating food that wasn't fresh-killed. Fresh killed? Mild. Getting older? Add a little bit of tabasco sauce. Getting rank? Pour in the cayenne. A side effect of that lack of refrigeration is that you had to catch your food locally because you couldn't go down to the corner market to pick up something from the cooler/refrigerated aisle. In follow-up to your question about paprika: we didn't use paprika that much because it wasn't grown locally and would have had to have been shipped in. But Cajuns were poor country people who had to live off the local available food sources. If you see a modern recipe claiming to be original to south Louisiana and it contains paprika, it is Creole and originates from a non-wetlands area.
Other spices commonly used in the area included file' which is derived from the plant that gives us sassafras. Tomatoes will grow anywhere that you have water, light, and soil, so they are common. Rice grows well where water ponds are abundant, and we can use certain types of cane syrup as sweeteners if needed. Salt is locally found (we have salt domes) and we can grow some types of fruit in this soil. Black pepper would have been imported initially so isn't quite as common as tabasco or cayenne peppers. This may be apocryphal but it is said that okra was introduced to the area by slaves who had used okra seeds as a hair decoration.
Styles include boiling, roasting, broiling, baking, frying - but since the people were "living off the land," they would cook based on what they could get. Except for wild hogs and goats, animal fat wasn't commonly available so deep-fat frying wasn't that common at first. Boiling is actually the easiest since we have abundant water that is potable once boiled thoroughly. Therefore, boiled and peppery seafood dishes would be considered authentic and old-style original to the area. The modern "crock pot" cooking methods that involve putting something on a long, slow boil came from the idea that we didn't have fancy-schmancy microwaves or intelligent ovens or high-tech, high-temperature ceramic tops. We could not cook anything fast, because wood-burning stoves were the only things we could use and they don't get as hot as the high-tech stuff. So we boil meat and use water-based immersion for a lot of preparation.
As an example, look at a New Orleans favorite: Red beans and rice with sausage. You boil the beans all day until they get caramelized. When it first starts to boil, add crushed or chopped (but not powdered) bay leaf to the beans and stir. Chop up the sausage and add it to the beans. Stir. When the beans have caramelized, keep cooking. (If this doesn't take hours, you are rushing it.) When getting ready to serve, boil the rice separately. Plate the rice. Ladle on the beans and sausage mix. This was a traditional Monday dish because Monday was laundry day. So you start the cooking fire, put on the beans, and then start washing. When your first washing batch is done, check the beans to be sure they still have water. Go do more washing. Check the beans. Do the wash ... you get the idea. Variations on this theme would put ham cubes in the beans and would then broil or pan-fry the sausage to be served beside the rice & beans. And this should tell you something about Cajun cuisine.
