Garden Compost:  MEdium fertility.  Dig in or mulch.

Green waste compost:  Low fertility.  Dig in or mulch.  Available from large-scale municipal recycling centers, likely low in nitrogen but high in potassium.

Commercial bagged compost:  Variable fertility.  Dig in or mulch.

Worm compost:  High fertility.

Strawy animal manures:  Medium to high fertility.  Must be well rotted before being dug into the soil.  Unfortunately, getting organic animal manure is difficult.

Spent mushroom compost:  Medium fertility.  Tends to be alkaline, so choose which plants to use it on with care.  Can be sourced from organic mushroom growers.

Leaf mold:  Low fertility.  Mulch or dig in, depending on age.

Straw:  Low fertility.  Source from an organic farm if possible.  Best as a mulch.

Bark chips and shredded prunings:  Lower fertility.  Best used as a mulch only, and on ornamentals, rather than food plants.  If dug in, they can rob nitrogen from the soil.  This caution also applies to horse manure with wood chips.