The aim of this paper is the analysis and selection of stock trading systems that combine different models with data of different nature, such as financial and microeconomic information. Specifically, based on previous work by the authors and applying advanced techniques of Machine Learning and Deep Learning, our objective is to formulate trading algorithms for the stock market with empirically tested statistical advantages, thus improving results published in the literature. Our approach integrates Long Short-Term Memory (LSTM) networks with algorithms based on decision trees, such as Random Forest and Gradient Boosting. While the former analyze price patterns of financial assets, the latter are fed with economic data of companies. Numerical simulations of algorithmic trading with data from international companies and 10-weekday predictions confirm that an approach based on both fundamental and technical variables can outperform the usual approaches, which do not combine those two types of variables. In doing so, Random Forest turned out to be the best performer among the decision trees. We also discuss how the prediction performance of such a hybrid approach can be boosted by selecting the technical variables.