From which category of elements would you choose to make a container that would not shatter if it dropped?

Okay. 
So the reason why a certain material would break upon impact is (to really, really dumb it down to save space) because the material is rigid, and not flexible. 

So things like glass and hard plastic are not good choices if you want a shatter-resistant container. 

Things like Metals are malleable, that means that it can be hammered into thin sheets. Metals are softer and more flexible than materials like glass or hard plastic, so the worst thing that could happen to a metal container when dropped is getting dented, but it won't shatter. 

As for where the metals are on a periodic table, take this paragraph from "Chemistry for Dummies": 
"In the periodic table, you can see a stair-stepped line starting at Boron (B), atomic number 5, and going all the way down to Polonium (Po), atomic number 84. Except for Germanium (Ge) and Antimony (Sb), all the elements to the left of that line can be classified as metals."