Oxbow is far better quality hay. It's probably the best thing you can buy in stores. They harvest and preserve it better. Online you can get bulk hay a ton cheaper than in little petstore bags as well as better quality since it does not sit out in the light for transport and store shelves. I just ordered 50lbs bluegrass from kmshayloft.com . They also have timothy. I think in 10lb, 25lb, and 50lb. You might be able to get different quantities if combining things. Shipping is high but you have to think of it per pound versus what you pay per pound in the store. Oxbowhay.com also has online vendors of their hay that you can buy in bulk. A cheaper way to get hay is to check your local feedstores. They often have good quality compressed bales, standlee is a common brand, for something like $20 per 40-50lb bale. Feed stores only have timothy or alfalfa and timothy is the most common cause of hay allergy. We both have allergies so we have to order the bluegrass online.
Properly stored hay is good for about a year. Dumping it in a box with no plastic that is not on a humid floor and with the top closed is best. Light and moisture will destroy hay the fastest. Letting the hay breathe through the cardboard or another method (they make special covers for transporting hay) will also help keep it fresh instead of trapping moisture and growing mildew.
Hay is most definitely not just hay. There are tons of things that go in to hay quality. The seed used, the soil amendments made to the field, the age and weather it's cut in, the drying process, turning process, baling process, and storing all impact hay. You make cheap hay by using cheaper varieties of seed that isn't as weed free, do not amend the soil through the years, cut it later so there is more grown there, methods like salt drying to avoid weather restrictions, and some places will put preservatives on their hay to keep it looking greener despite light exposure. Oxbowhay and kmshayloft do not do any of that.