Couldn't sleep tonight, got out of bed, decided to see what my old buds on the Flower/Garden board were up to. This was first thing I saw and I was just reading about this very same thing while trying to get to sleep tonight!
Straw - doubtful protection. We have all probably seen silage cutters, equipped with blowers,throwing out straw as a mulch over newly seeded highway shoulders. This looks like a good idea for the home lawn -- and it does have value in establishing rough lawns in areas inaccessible to water -- but for home lawns it is not good practice. Straw can be used in semiarid regions or during droughts as a crutch for a new seeding. Ordinarily, however, the problems it creates will be worse than those it solves. Water alone will do a much better job. True, straw keeps soil moist and cuts the need for irrigation. The difficulty lies in organic matter left behind by the straw. For one thing, as it decomposes, bacteria use up nitrogen from the soil. Often straw-mulched lawns start growth rapidly, but turn yellow after a few rains. Water has dampened the straw enough to start decay, and bacteria draw nitrogen from the soil in order to work on the mulch.
Later, if the straw was heavy enough to do its work, there will be a layer of duff in which fungi will multiply easily. Then fungi may move onto the grass. So, if straw is used, it should only be applied to areas open to full sun from dawn to sunset. Actually these are conditions usually found where this methoid is used -- on the shoulders of roads. If strawing seems to be the only way to establish a home lawn under difficult conditions, be sure the material is run through a silage cutter or hammer-mill to break up long straggly wisps.
For smallers areas, buckwheat hulls, rice hulls, or horticultural vermiculite can be used as mulches. They are too costly for larger lawns.
Adding nitrogen at the rate of one pound per thousand square feet, after the first mowing, will speed the decay of organic mulch. Vermiculite is mineral and presents no problem.
That was from a book dated 1971 and I found some of the stuff in it no longer the norm. But decided to post it for you to take as you see fit.
I, myself, would go with the peat moss.