Healthy soils gives us healthy, tasty food, it does not matter on scale. Creating and maintaining healthy soils should be the main focus of anyone growing plants. Healthy soil will grow the healthiest plants with the least amount of work on our part.
The easiest way to guide your decision making process is to follow the principles of soil health. They are reducing tillage, reducing the use of synthetic inputs, increase plant diversity, livestock integration, and keeping a plant's living root in the vegetative stage for as many days as possible. For a garden, livestock integration is not a possibility so for this discussion we will ignore it.
Cover crops can be used in four main ways: preseeding, intercropping or relay cover cropping, post harvest, and full season. Preseed cover cropping is where a cover crop is seeded early in the spring, then terminated before seeding the garden. This could be to loosen up the soil, stimulate soil biology, suppress weeds, or dry out the soil. Intercropping or relay cover cropping has a cover crop growing with the vegetables throughout the growing season. It can die at the first frost, late into the winter, or even over winter. Intercropping can also be described as Milpa garden, growing many if not all of the garden species together in a mix. Post harvest cover crop occurs after the vegetables are harvested. Full season covers would replace a year of fallow.
When picking species for the cover crop, look at adding functional plant groups to the mix. The main five are grass, legume, forb, Brassica, and non Brassica. Within each group look for warm and cool season species, annual, biennial, and perennial options. Each of these have their own set of root exudates that supports different microbes in the soil.
When plants are in the vegetative stage, they can release up to 80% of the carbon it captures through photosynthesis into the soil as root exudates. By having a plant like Italian ryegrass will continue to feed the soil throughout the growing season. Annual plants only feed the soil biology for approximately forty days. As the plant root exudates continue to be released, soil microbes will continue building soil and soil structure. With improved soil structure, the roots are able to move effortlessly through the soil without requiring extra energy being drawn from the plant. Water infiltration will improve, nutrient cycling will speed up, weeds will disappear, and life will come back into the soil once good soil aggregation is created.
Legumes are typically a good plant group to include in cover crop mixes. They fix nitrogen, are highly mycorrhizal minus lupins, and they offer low levels of competition. Species like crimson clover, Persian clover, subterranean clover, vetches are good annual options. Grasses are good to add later in the year, or after harvest. Species such as oat, annual ryegrass, millet are common annual options. Italian ryegrass has poor winter hardiness where winter wheat and winter triticale are better when looking at biennials. There are a fair amount of forbs available but Phacelia is an annual that is very popular, especially for the pollinators. Chicory is a biennial plant that helps build soils. Non brassicas include species like flax, sunflower, buckwheat, and beets. Each brings something different to the table when it comes to building soil. Brassicas are predominantly biennials, minus radish. They are nutrient scavengers that do not support mycorrhizae fungi. Normally, they are seeded post harvest as to not compete with the vegetables. They typically have high frost tolerance so will stay green very late into the fall or even into winter.
Picking species is significantly easier if you have goals in mind. Knowing how plants grow will indicate what species should be used given the issues and your goals. The easiest thing to do is to keep something green and growing throughout the entire growing season, and reduce the amount of tillage that is done. Keep the soil covered and do not garden naked.