Readability research has a long and rich tradition, but there has been too little focus on general readability prediction without targeting a specific audience or text genre. Moreover, although NLP-inspired research has focused on adding more complex readability features, there is still no consensus on which features contribute most to the prediction. In this article, we investigate in close detail the feasibility of constructing a readability prediction system for English and Dutch generic text using supervised machine learning. Based on readability assessments by both experts and crowdsourcing, we implement different types of text characteristics ranging from easy-to-compute superficial text characteristics to features requiring deep linguistic processing, resulting in ten different feature groups. Both a regression and classification set-up are investigated reflecting the two possible readability prediction tasks: scoring individual texts or comparing two texts. We show that going beyond correlation calculations for readability optimization using a wrapper-based genetic algorithm optimization approach is a promising task that provides considerable insights in which feature combinations contribute to the overall readability prediction. Because we also have gold standard information available for those features requiring deep processing, we are able to investigate the true upper bound of our Dutch system. Interestingly, we will observe that the performance of our fully automatic readability prediction pipeline is on par with the pipeline using gold-standard deep syntactic and semantic information.