The most popular thing going around these days are fleece cage liners. You can make them or buy them; they are reusable, washable and save money over time though it may be a little costly to get started. Just google Guinea Pig Fleece and a huge amount of sites and videos will come up. If you choose to buy from someone, you'll find they only make for the C&C cages and the Midwest one as they think those are appropriate sizes. There are a few who will custom make, but it's rather expensive.
I've never tried fleece but would really like to. CC thinks she can do the sewing part (I'm not sewer) but I would really like to test it first. After some research I came across this:
What's happening here is that the person put absorbent material on the bottom and then just used fleece over the top securing it with the cage. Great Idea! So I'm going to give that a try!
Not all fleece is created equal, so make sure to read the websites on the proper kind to choose and make sure to wash it until it absorbs!
When it comes to shaving beddings do not use Cedar (the oils are bad for piggies), Pine only if it says it is "kiln dried" or Aspen. The best bedding in my opinion is CareFresh....it kind of looks like shredded cardboard! It can get pricey though so you may want to do a mix of CareFresh and Aspen.
Regardless what you choose, remember - piggies need a clean and dry environment.