Your best bet is to talk to a horse person, they buy it frequently and seem to know all about the cuttings. Also, they buy it from a feed store that communicates with the grower, or in some cases, they feed stores are the growers. My dad (who is a horse person), explained the cuts to me. He said the first cutting is premium for horses, this cut has the "heads" on it. It's the purest timothy, and it's also the hardest. So, you'll see lots of timothy heads on thin, hard, stem type things. The second cutting is also on the hard side, and it's not as pure (at least it's not as pure from the feed stores from which I've bought it), this is because it is blended with (I call it) the "brown" hay, my bunnies bypass the brown stuff, so it's more for me to clean up, they don't even eat it. The third cutting would be the softest, and the most blended. Though, I think Oxbow is more selective and they don't blend their Timothy with other types of hay like the feed store does. Oxbow is the best brand nutritionally. I believe it's hand selected as well, and this explains why it's not blended.
I buy the 50lb Oxbow Western Timothy. From the quality, I can tell that this hay is first cutting, it has a lot of heads and it is hard. I think it seems freshest in the spring; I think this because the color is nice and green and the smell is that of fresh hay. You can roughly assess the age and quality by the smell and color. I feel that it's not as fresh in the fall/winter, but it's still great.
I don't know about Guinnea Pigs, but for adult bunnies, it's important that they eat Timothy Hay, not alfalfa or anything else on a regular basis. Timothy is what they need nutritionally. I have noticed that the big BAGS (not sure the weight), and NOT the 50lb box, of Oxbow Timothy are softer, and it seems like they are likely 2nd cutting, possibly even 3rd cutting, but still very pure. I've noticed that these bags are far fresher from this site than in the pet stores. I think the shelf life must be very long in some pet stores, because I've definitely accidentally bought old, browning hay in the stores.