As the others say, cardboard shoeboxes would not be the slightest bit escape-proof! Plastic ones would have sharp bits if chewed (needs to be the right kind of plastic) and anything with square corners and seams like a plastic shoe box could cause injuries if chewed). As a toy in a playpen it would be fun using shoeboxes linked with toilet rolls.
Even a wood cage or plastic cage base can be chewed through by a determined hamster!
I would suggest looking at the Alaska cage on Zooplus. It's a good price - about £33 - and a good size for a hamster.
Alaska Hamster Cage | Free P&P on orders £29+ at zooplus!
You could maybe make a bin cage a bit cheaper than that if you have all the tools already, but some bins (that are big enough) cost more than the Alaska cage.
A detolf is a good option! Costs £40 - tip it on it's side and leave the door off and it's a large glass tank. You need to make a lid (or two smaller lids) out of wood and mesh.
https://www.google.co.uk/search?q=Ha...w=1366&bih=608