Many use peat moss. It's organic. It is water repelent when dry and care must be taken to get it wet, but it makes a good seed cover and it indicates when it is drying by changing color- warning you when you need to water to keep the seed moist. Remember to always keep the seed moist,and only keep seed moist not soaked.

Compost can also be used as a topdress. I have used shredded straw in the past, which is easy to spread, doesn't need to be removed, adds OM, and if can offer some protection from washout. That is the only straw I would recommend.

My biggest complaint about straw (I have only had expeience with bailed as it is what is readily available in my area) is that it is susceptable to being blown around by a breeze and wherever it clumps, if not quickly respread, it impedes growth. Plus bailed does not decompose quickly. I have never used shreded and shreded may have different outcomes.

OP: How heavy would you spread the peat moss?

Would Compost be spread at the same rate?

No topdressing should be spread thicker than 1/4 over seed. You want to use the minimum necessary to cover the seed,

1/4 inch