Machinery for data analysis often requires a numeric representation of the input. Towards that, a common practice is to embed components of structured data into a high-dimensional vector space. We study the embedding of the tuples of a relational database, where existing techniques are often based on optimization tasks over a collection of random walks from the database. The focus of this paper is on the recent FoRWaRD algorithm that is designed for dynamic databases, where walks are sampled by following foreign keys between tuples. Importantly, different walks have different schemas, or "walk schemes", that are derived by listing the relations and attributes along the walk. Also importantly, different walk schemes describe relationships of different natures in the database. We show that by focusing on a few informative walk schemes, we can obtain tuple embedding significantly faster, while retaining the quality. We define the problem of scheme selection for tuple embedding, devise several approaches and strategies for scheme selection, and conduct a thorough empirical study of the performance over a collection of downstream tasks. Our results confirm that with effective strategies for scheme selection, we can obtain high-quality embeddings considerably (e.g., three times) faster, preserve the extensibility to newly inserted tuples, and even achieve an increase in the precision of some tasks.