Accurate tool wear prediction is essential for maintaining productivity and minimizing costs in machining. However, the complex nature of the tool wear process poses significant challenges to achieving reliable predictions. This study explores data-driven methods, in particular deep learning, for tool wear prediction. Traditional data-driven approaches often focus on a single process, relying on multi-sensor setups and extensive data generation, which limits generalization to new settings. Moreover, multi-sensor integration is often impractical in industrial environments. To address these limitations, this research investigates the transferability of predictive models using minimal training data, validated across two processes. Furthermore, it uses a simple setup with a single acceleration sensor to establish a low-cost data generation approach that facilitates the generalization of models to other processes via transfer learning. The study evaluates several machine learning models, including transformer-inspired convolutional neural networks (CNN), long short-term memory networks (LSTM), support vector machines (SVM), and decision trees, trained on different input formats such as feature vectors and short-time Fourier transform (STFT). The performance of the models is evaluated on two machines and on different amounts of training data, including scenarios with significantly reduced datasets, providing insight into their effectiveness under constrained data conditions. The results demonstrate the potential of specific models and configurations for effective tool wear prediction, contributing to the development of more adaptable and efficient predictive maintenance strategies in machining. Notably, the ConvNeXt model has an exceptional performance, achieving 99.1\% accuracy in identifying tool wear using data from only four milling tools operated until they are worn.