Organic: formerly alive
More beneficial: stuff that will rot/break down quickly, such as
leguminous green manure (vetch, clover, etc)
Less beneficial but still good (legume = nitrogen, ie free fertilizer):
ANNUAL rye grass (do not use perennial rye grass), buckwheat - sow it,
let it grow for a bit then turn it under.
Old bean/pea plants, etc. Do not use plant remnants of diseased
plants; some people also do not use old brassica remains; problems in
your old plants will end up in your garden.
Do lots of reading over this group for beginner material, and even
check some gardening books out of your local library. A couple for you
(there must be a reading FAQ somewhere):
The New Organic Gardener, by Eliot Coleman
The New Victory Garden, by Bob Thompson
Cheers, welcome, and good luck!