The traversal-based approach to execute queries over Linked Data on the WWW fetches data by traversing data links and, thus, is able to make use of up-to-date data from initially unknown data sources. While the downside of this approach is the delay before the query engine completes a query execution, user perceived response time may be improved significantly by returning as many elements of the result set as soon as possible. To this end, the query engine requires a traversal strategy that enables the engine to fetch result-relevant data as early as possible. The challenge for such a strategy is that the query engine does not know a priori which of the data sources discovered during the query execution will contain result-relevant data. In this paper, we investigate 14 different approaches to rank traversal steps and achieve a variety of traversal strategies. We experimentally study their impact on response times and compare them to a baseline that resembles a breadth-first traversal. While our experiments show that some of the approaches can achieve noteworthy improvements over the baseline in a significant number of cases, we also observe that for every approach, there is a non-negligible chance to achieve response times that are worse than the baseline.