What determines the variety of paprika to use in recipes?
If a recipe didn't specify which type of paprika to use (and I've never seen one that didn't) I would default to a 'sweet mild' paprika. Sweet refers to 'not chilli hot' rather than anything to do with sugar. Smoked paprika is a very particular ingredient used in very few cuisines so I wouldn't think of it as just a variant or substitute for the other paprikas. 

The other clue about which to use will be in the rest of the recipe. Is it a spanish or basque recipe? Then smoked is likely what they mean. Is it Croatian/Serbian? Then it is sweet mild. Does the recipe include chilli as a spice separately? Then they likely won't be asking you to double up by using hot paprika too, use mild. The quantity the recipe calls for will also be a clue. Smoked &amp; hot paprikas are very strong, so I'd expect to see a pinch or 1/4 teaspoon listed in most cases, whereas mild paprika is often used to add colour as well as flavour so you might see greater quantities used.