I make this recipe with British pork sausages - i.e. ground/minced pork in a sausage casing and purchased uncooked. However, you can use a variety of different sausages based on your preferences.
You could substitute chicken, beef or lamb sausages, or even vegetarian ones. Just bear in mind that the type of sausages I use are usually around 1 inch/2.5cm thick. If you use a thinner sausage, then you can reduce the cooking time to prevent them from burning.
If you use a cured sausage that doesn't necessarily require cooking, such as Spanish chorizo or salami then I would add the sausage 10 minutes before the end of the cooking time instead, to prevent it from drying out. As these sausages are very rich you probably want to use a smaller amount and use slices instead of the full sausage.
You could also use smoked sausage. Such as frankfurters or hot dog sausages, but again I would only add them towards the end of the cooking time.