I'm learning a lot about cover crops as soil conservation, and was wondering what would be the best choices for my garden, in a Minnesota, zone 4a climate? It should produce good amounts of mass to plant on top of in the garden.
Answering for your location (Minnesota, zone 4a), so as to keep this answer contained. In your climate, you'll get the most biomass from a summer season cover crop. Of course that will make it hard to grow food crops, unless you stagger beds, and use more square footage than you would need for a single food crop.
The winter cover crops that aren't winter killed in your area, can be allowed to go to flower in the spring if derired, before being turned in. Rememer than many decaying plants have allelopathic effects for a few weeks after being turned under. This is not the case if the cover dies completely before being turned under (although this will lose most of the nitrogen from the green matter).
You can create mixes, so that you have a more diverse growth. Many grasses and legumes grow well together, for example. In my climate, where rye lives through the winter, a rye and vetch planting is common.
Early spring planting (plant as soon as the ground is workable. Till in during first flowering)
Late spring/summer planting (full season crop - growth until frost)
Fall planting (plant after it cools down, 4-6 weeks before the ground freezes, the longer the better)