It doesn’t matter as long as the hay is kept dry and smells fresh, without any trace of mould. All grass hays are good for adult buns, baby rabbits can have alfalfa as well, but adults should only have have grass hay. Timothy is great, but there is also orchard and oat hay and rye grass and various types of meadow hays. Some humans with pollen-allegies react to timothy, if that’s the case orchard is generally a better choice. I buy some pet-store hay, some Oxbow hay and when I can get it, good quality locally produced hay for milk-cows or horses. Bunnies can be particular about hay, so you might have to try different varieties before you find one that your bun likes.
As for choking, the biggest risk is with pellets. For that reason it can be a good idea to scatter the pellets so the bun is slowed down by having to search for the food, or to serve pellets in a food-ball, again to slow the bun’s eating down.