In order of my preference...

1) Leaves - lots of various nutrients and micro-nutrients.
2) Straw - not a lot of nutrients but is high in lignin so not a great C for sustained high temperature composting.
3) Wood chips - great for aeration but unless the bark is in there, not a lot of nutrients.
4) Paper/cardboard/sawdust - works okay as a C but once again not a lot of nutrients and natural aeration can be difficult due to compaction.

If great compost is your goal, leaves are best. If just getting the N to compost without odours, then any C will do.

I just built some windrows using wheat straw because that's what I have and I had about thirty tons of grass clippings I had to do something with. It got hot (162) the next day but down to 130-140 after a couple of days.

Lloyd

P.S. Can anyone please turn off the rain for a couple of weeks? Pretty please. :-(

I'd put sawdust ahead of wood chips; it seems to combine very well with manure. Chopped straw seems to work great with food scraps and plant residues, though it makes sense that leaves (preferably chopped) are higher in nutrients because trees pull them up from deep in the ground. I haven't had much luck with wood chips or paper products and avoid them in my compost.

A wide variety of materials provides you compost with a wide variety of nutrients. Some plants accumulate different, especially micro, nutrients then other plants and the best way to ensure you have a wide variety of nutrients to put into your soil use as wide a variety of materials as possible.