The first two are both correct. The first version is stronger than the second - one would likely put extra emphasis on the then. To the native English speaker, this will mean something similar to 'only then should they be selected'.
The third sentence is incorrect, since the second part does not have a subject. Since an if/then construction relates two complete sentences, both should usually (see below) have a subject and main verb. For example, one could also say 'If the hamburgers are black, the barbecue should be left to cool' - two completely different subjects! So, one cannot assume the subject to be the same in both parts of the sentence.
As Araucaria mentioned, there is a possibility to drop the repetition by using the construct if [property of subject], [main clause]. For example, if black, they should be selected. It's basically a shorter version of 'If the subject is [property of subject], [main clause]'. Example: 'If the button is red, the button should be pushed' could be shortened to 'If red, the button should be pushed'. Care should be taken not to say things like 'If red, you should push the button' - then you're saying the person pushing the button should be red, not the button!
An alternative construct without repetition would be 'Those that are black, should be selected'.