We present a new type of large-scale computational screening approach for identifying promising candidate materials for solid state electrolytes for lithium ion batteries that is capable of screening all known lithium containing solids. To be useful for batteries, high performance solid state electrolyte materials must satisfy many requirements at once, an optimization that is difficult to perform experimentally or with computationally expensive ab initio techniques. We first screen 12 831 lithium containing crystalline solids for those with high structural and chemical stability, low electronic conductivity, and low cost. We then develop a data-driven ionic conductivity classification model using logistic regression for identifying which candidate structures are likely to exhibit fast lithium conduction based on experimental measurements reported in the literature. The screening reduces the list of candidate materials from 12 831 down to 21 structures that show promise as electrolytes, few of which have been examined experimentally. We discover that none of our simple atomistic descriptor functions alone provide predictive power for ionic conductivity, but a multi-descriptor model can exhibit a useful degree of predictive power. We also find that screening for structural stability, chemical stability and low electronic conductivity eliminates 92.2% of all Li-containing materials and screening for high ionic conductivity eliminates a further 93.3% of the remainder. Our screening utilizes structures and electronic information contained in the Materials Project database.