Multi-behavior recommender systems in e-commerce leverage heterogeneous user actions such as page visits (pv), favorites (fav), cart additions (cart), and purchases (buy) to improve recommendation accuracy, particularly for sparse target behaviors. This study aims to develop an efficient and unified fusion framework that integrates nonlinear interaction modeling, sequential representation learning, and attention mechanisms to enhance purchase prediction. We propose two hybrid architectures: RecNeuLSTM, which combines Neural Matrix Factorization (NeuMF) with Long Short-Term Memory (LSTM), and its extended variant RecNeuLSTrans, which further incorporates a Transformer encoder. In the proposed framework, NeuMF captures static and nonlinear user–item interactions, LSTM models short-term sequential dependencies among behaviors, and the Transformer captures longer-range contextual relationships via self-attention. Extensive experiments conducted on two public benchmark datasets, Tianchi and Tmall, demonstrate that the proposed hybrid models consistently outperform strong baseline methods under the same evaluation protocol. In particular, RecNeuLSTM and RecNeuLSTrans achieve average relative improvements of approximately 85% on Tianchi and 60% on the larger and more imbalanced Tmall dataset with respect to purchase prediction metrics. These results indicate that jointly modeling static interactions and dynamic multi-behavior sequences is an effective strategy for improving purchase prediction in real-world e-commerce recommendation scenarios.