I think Rubberwood is good too - I've seen a few things made of Rubberwood including the Living World Eco Habitat. If you're just wanting to make wood items for the cage though it's probably just easier to use kiln dried untreated pine. It should be available from big hardware stores. Actually there are some quite good wood houses you can buy. The one I have comes in 3 different sizes and has no nails. I got the guinea pig sized one for Charlie and it's nicely finished and not too expensive. The Hamster sized one is quite small and probably only suitable for a dwarf.
Wooden House for Guinea Pigs, 28 × 16 × 18 cm: Amazon.co.uk: Pet Supplies
The door is quite big so I put a bendy stick bridge over it which makes it dark inside and a bit like a mini labyrinth.
VioletandMe - if you are thinking of building a cage out of wood, I would have a look on ebay - I've seen all kinds of fairly cheap furniture made out of solid oak - sideboards and cabinets with doors, that could be converted and you'd have good hardwood at a good price. They'd probably need sanding down though to get rid of any polish.