Hay over newspaper is what I've always used for my piggies, though now I also buy sacks of straw-based pellets from Zooplus to sprinkle over the newspaper and under the hay. They help to absorb the moisture and also do a pretty good job at keeping down odours. I do a full cage clean twice a week, which usually seems sufficient. It certainly is easy just to roll up the old bedding, and replace with new, but I do give the cages a clean before putting in the fresh stuff, just a quick clean with a small animal spay disinfectant and paper towels if I'm in a hurry, or when I've got more time I wash them out with a safe disinfectant called Conficlean2, then rinsing and drying thoroughly. I did for a time consider using fleece, as it seems to be so popular these days, but came to the conclusion that I'd never keep up with all the poop collecting, and that I didn't want all the extra washing. Some of the soiled hay goes on our compost heap, so the little piglets are helping the fertility of the garden, clever things!
There's no doubt that the pigs love being bedded down in hay. They're always so excited when they've just been cleaned out, and have got so much hay to forage and burrow in. They do get given extra fresh hay for nibbling at least once a day. The only downside from my point of view is that hay makes a bit of a mess, (ends up all over the house somehow!) but it makes the pigs happy, and that is the most important thing. I don't find it too expensive either. I don't expect I'll ever change to any other form of bedding, unless I ever have a piggy that needs a completely dust free bed from a medical point of view, in which case I would use fleece or vet bed, and happily put up with the washing!