They should have a large wheel (12 in.), lots of wood tunnels, houses, etc. to chew and hide in. Mine also have ferret hammocks, pieces of apple branches to chew, toilet rolls to play with, pumice stones, paper towelling to shred, mats made out of straw to chew up and drag around, etc. etc.
As for holding, mine don't like to be held much. You should visit a site like the deguworld forum and/or degutopia. There are many degu owners there with lots of great ideas for entertaining your degus as well as great advice on cages, food, handling, etc.