Despite the increasing interest in sequential transfer optimization (STO), a comprehensive benchmark suite for systematically comparing various STO algorithms remains underexplored. Existing test problems, which are often manually configured and lack scalability, can result in biased and nongeneralizable algorithm performance. In light of the above, we first introduce four concepts for characterizing STO problems (STOPs) in this study and present an important feature, namely similarity distribution, to quantitatively delineate the relationship between the optimal solutions of source and target tasks. Subsequently, we present general design guidelines for STOPs and introduce a problem generator that demonstrates strong scalability. Specifically, the similarity distribution of a problem can be easily customized through a novel inverse generation strategy, allowing for a continuous spectrum that captures the diverse similarity relationships present in real-world scenarios. Lastly, a benchmark suite comprising 12 STOPs, characterized by a range of customized similarity relationships, has been developed using the proposed generator and will serve as a platform for examining various STO algorithms. For instance, biased transferability representation, irregular mapping learning behaviors, and performance improvements unrelated to search experience are significant empirical findings that previous benchmarks failed to reveal, yet can be effectively identified through our test problems. The source code of the proposed problem generator is available at https://github.com/XmingHsueh/STOP-G.