Goal setting is a commonly employed game element and an implicit effect of gamification. Research in goal-setting theory has found specific and difficult goals to increase the effectiveness of mobile health interventions. Previous work has indicated a lack of research about the impact of different types of goals, especially those with time constraints. This work introduces a goal-setting mechanism with two types of goals, namely continuous and time-bound, to the Sleep Revolution app, a mobile application for sleep healthcare that enables users to set goals regarding several activities they track in the app's sleep diary. The implementation follows concepts and recommendations from previous work. To assess and compare the effects of the different goals on user compliance with health recommendations, a four-week randomized controlled trial was conducted. In a second step, the feasibility of extending the mechanism with personalized goal recommendations based on the data collected in the trial is explored. Different machine learning algorithms are compared regarding their applicability to this problem and their potential effectiveness.