Lodash's "sortBy" method helps you sort data in your collections and "sortedIndex" helps you find where to place new data. In this video, John walks you through how to use each of these methods and how they can work together.
He keeps a suite of benchmarks here:
Looks like they're down for the moment.
As for "index then splice" vs. "push then sort", I'm pretty sure the answer is "it depends" on your data.