Chloe and George only got paper towel rolls. Their glues have never been a problem. Food boxes tend to have too many inks and some are coated. Instead of giving food boxes and toilet paper rolls to them, I grew transplants in them (Great if you're a gardener!) and planted the entire roll or cut the box prior to planting the entire thing. Shipping boxes are great in your compost bin or between rows to control weeds. My birds didn't even miss them!
I found that 1"×2" cut up into cubes and drilled made great hanging and chew toys for them. A larger bird might need a 2"×4". Just be careful to buy heat-treated NOT chemical-treated wood and attached bells to the ends. (My birds loved bells!) Most towns and cities have lumber-cutting yards that are very happy to sell you untreated scraps! These wood chews can easily be dyed with vegetable dyes for color if you must. Usually, dowels are treated and should be avoided unless bought from bird-safe supplier or you can simply cut up unused perches.
I also regularly visit the baby section of our dollar store and the APS thrift store. Remember, a bird can destroy an expensive toy as quickly and easily as a cheap toy!
