Many people use a cage with a wire bottom and a tray underneath to catch the droppings. Guinea pigs will chew on almost anything and having wood chips or other substrate could cause some serious problems if they eat it.
I used to show guinea pigs. We kept them in wire cages, but you must have at least a smooth board for them to sleep on and give their feet a rest from being on the wire. This helped keep their coats cleaner and was easier maintenance with having a large number of guinea pigs. Wood chips are ok in the drop pans, but never use cedar. The dust from wood chips can cause respertory problems so use with caution.
The best choice however, is CareFresh recycled paper bedding. It is biodegradable and ok if they eat it. You can get it pretty cheap at Walmart or watch for sales at your petstore.
Thanks for the reminder about a resting place for the feet. I did that with my piglets and they were very good about using another corner for potty. They weren't keen on soiling their "bed."
I agree about cedar chips. Pet stores sell them and people buy them thinking they smell so nice. But all those aromatic oils are a problem for small animals.