Dead, dry leaves are in the 'browns' category, while living green leaves contain abundant nitrogen and are considered 'greens'. They can burn plants if applied when fresh, so be sure they get well composted. Some manures may contain weed seeds. Fresh manures can get a compost pile to heat up quickly, and will accelerate the decomposition of woody materials, autumn leaves, and other 'browns'. Be sure to wet the straw, as it is very slow to decompose otherwise.
Straw is definitely a 'brown' and also requires mixture with 'greens' to break down quickly.
Many types of weeds and old garden plants can be composted. Avoid weeds that have begun to go to seed, as seeds may survive all but the hottest compost piles. Others, especially from coniferous trees, will take longer to decay. Stir sawdust thoroughly into the pile or use very thin layers. Coarse wood chips will very slowly decay, and are probably better used as mulch unless you have lots of time to wait.