In general, there are two kinds of removable denture: Complete and Partial, indicating whether the denture replaces all or only some of the teeth.
Restore or improve masticatory function (eating)
Restore or improve phonetics (speech)
Restore or improve esthetics (smile and appearance)
Keep in mind that the patient will need time to ...
The question of augmentation-or-prothesis first is difficult to answer, and may even be based on the personal physiology of an individual. As such, health.se can't address that question.
Regarding the second question, "can chin-augmentation affect the individual's bite...", there's a study done with porous hydroxyapatite (not sure if chin-augmentation ...