I think it's normal for them to mess/peck with the shavings. It is, after all, new. As long as they're not actually eating a lot of it, they should be fine. My 3 week olds still peck at their bedding but they're not eating it persay.
long grass clippings and hay can cause impacted crops so i'd avoid those for chicks. After they learn what food is, shavings should be fine. They will pick and scratch, but not likly eat them up like food and cause an impaction. A bowl of sand or dirt from their future run would be a good thing for them to gain immunities to the stuff outside, and for grit.
I have my chicks on shavings, but since they enjoy digging and scratching so much I found some large old Tupperware lids and twice a day (feeding time for the big hens) I put a scoop of chick feed on them and place them in the brooders so the little ones can scratch. They love it - - it's like a chickie dance floor, and all the little ones get out there and jitterbug around on the plastic until every last bit of food is gone.
This gets them on a big chicken schedule (although they have free choice in their feeders), it gives them something to do besides pick on each other, they stay on their balanced food ration and they get a bit of exercise in the brooders. I start doing this at one week of age.
My feed store recommended peat moss in the brooder to start. I used it in the first rabbit cage I started them in then moved the 10 chicks to the 169 gal stock tank I'm using and put peat moss in that as well however when they really learned to scratch at 1-2 wks, I had a fine black coating of dust covering everything. I then covered the peat moss with a bag of shavings.
They will still scratch down through the thick layer of shavings to the peat moss and take little dust baths in it.
I would use the peat moss again when the chicks are tiny because they can scratch it, they didn't eat it, it obsorbed the droppings, and it provided good footing for them. Great sprinkled on the garden when done with it.