Data is the engine of modern computer vision, which necessitates collecting large-scale datasets. This is expensive, and guaranteeing the quality of the labels is a major challenge. In this paper, we investigate efficient annotation strategies for collecting multi-class classification labels for a large collection of images. While methods that exploit learnt models for labeling exist, a surprisingly prevalent approach is to query humans for a fixed number of labels per datum and aggregate them, which is expensive. Building on prior work on online joint probabilistic modeling of human annotations and machine-generated beliefs, we propose modifications and best practices aimed at minimizing human labeling effort. Specifically, we make use of advances in self-supervised learning, view annotation as a semi-supervised learning problem, identify and mitigate pitfalls and ablate several key design choices to propose effective guidelines for labeling. Our analysis is done in a more realistic simulation that involves querying human labelers, which uncovers issues with evaluation using existing worker simulation methods. Simulated experiments on a 125k image subset of the ImageNet100 show that it can be annotated to 80% top-1 accuracy with 0.35 annotations per image on average, a 2.7x and 6.7x improvement over prior work and manual annotation, respectively.