I amend the gardens with greensand (for the micronutrients like
iron rather than forthe potassium) and rock phosphate about
every 5 years, and I use composted leaves, grass clippings, etc,
but I have had the best results with aged horse manure, either
spread a foot deep over the whole garden and turned in or
mixed with compost and soil in individual planting holes
for tomatoes. (Rabbit, llama, and alpaca manure would be good
choices, too, but I have not had them available in the same
quantities as horse manure.) Chicken manure I mix into grass/leaf
compost and let it cook a few months before using it.
These days, it is necessary to test manure for undigested
herbicides before using it:
http://whatcom.wsu.edu/ag/aminopyralid/bioassay.html
(I use liquified kelp, fish emulsion, dissolved humic acid,
and molasses when watering in transplants in the spring, too.
After years of organic soil amendments, the top foot of soil
is quite fertile, so if I do not have one or more of those
in spring when it comes time to plant, it is not a showstopper.)
My most effective winter cover crops in terms of growth the
next summer after turning the top growth in have been a mix
of bell beans (fava bean relative) and hairy vetch. I alternate
and use winter rye some years (depends on what the soil is
like exactly; winter rye does a good job of filling the top foot
of soil with roots and provides a lot of top growth for mulch
the next summer, while the bell beans and hairy vetch add
more nitrogen to the soil). The sprouted bell beans and vetch
are popular with the local squirrels in fall, so there is a lot of
attrition. (I think of it as natural thinning.)
edit:
One thing about winter rye and hairy vetch: they both flower late,
last week of April up here. That is when one typically wants to
cut them, to avoid having them become summer weeds. If you
have an early crop to plant, the cover crop is in the way.
(Not a problem with bell beans, you can cut them down any
time.) Where you need to plant something before the winter rye
and hairy vetch have flowered, one might be better off with a
fall cover crop that is winter killed, so you can turn it under or
plant right through the dead top growth the next spring.