You need a long strand grass hay for your pigs, to keep their teeth ground down and their guts moving normally. Long strand grass hays include timothy, brome, orchard, meadow and blue. Organic or not is up to you -- the nutritional value of the hay is the same, and hay isn't grown with a terrific amount of pesticides.
Alfalfa is a legume, like peas, and shouldn't be the only hay fed to pigs. It's suitable for supplementing the diet of pregnant/nursing sows and pups because it has a fairly high calcium content, but should accompany grass hay.
If you can find a local farmer who grows grass hay, that's the cheapest way to get the hay. You can buy a bale for what you'd pay for less than 10 pounds in a pet store. The middle-priced way is to order in bulk, either online or through a store that will order a big (40-50 pound) box for you. By far the most expensive way to buy it is in the bags at the pet store. You'll also get a much poorer quality of hay that way.