In this paper, we provide two data-driven algorithms for learning compressive sensing measurement matrices with Gaussian entries. In contrast to the ubiquitous i.i.d.~Gaussian design, we associate different variances with different signal entries, so that we may utilize training data to focus more energy on the ``most important'' parts of the signal. Our first algorithm is based on simple variance-proportional sampling (i.e., place more energy at locations where the signal tends to vary more), and our second overcomes limitations of the first by iteratively up-weighing and down-weighing the variance values according to reconstructions performed on the training signals. Our algorithms enjoy the advantages of being simple and versatile, in the sense of being compatible with a diverse range of signal priors and/or decoding rules. We experimentally demonstrate the effectiveness of our algorithms under both generative priors with gradient-based recovery and sparse priors with l1-minimization based recovery.