Just go check out what they have, look for large chunks if you can find it, otherwise the smaller stuff will work just fine (it takes longer for the bigger chunks to break down, which is good) Steer clear of cedar and mulch that is dyed.
Where are you located in general? Climate matters. As far as the grass goes it won't last long, they'll have it scratched up and eaten in no time. Chickens poop, a lot, they never stop, not even when sleeping, so keep this in mind. Personally I would add some wood chips or mulch to the run, they...