Knowing the type of hay you have is useful, although most are perfectly suitable for feeding in unlimited quantities. Legume hays - such as alfalfa - are too high in calcium and protein for adult pigs, so you need to be aware if the hay contains alfalfa. Legume hays are normally marked, and most local suppliers/farm shops will sell meadow or timothy hay by the bale, so it is very likely that you have a normal grass hay which is ideal to feed.
Meadow, timothy, orchard grass, rye, oat and brome are all types of grass hay. The greener the hay the better, so do go with the highest quality you can find and afford. A combination of hays will encourage a higher intake of hay, which is good for digestion and dental wear.