Make sure the hay is weed and seed free, or you'll cause more weeds than you'll prevent. And only get the hay when you're ready to use it. I mean really moldy. We're talking mushrooms and big clouds of mold here. Start tomatoes, peppers, broccoli and things like that inside.
Herbs are okay, too.
But please keep your peas, beans and lettuce out of the greenhouse. Friends don't let friends make the same mistake they did. You can plant peas, beans and lettuce right outside and pretty early, too. Rotate your crops so you aren't taking the same things out of the soil each year. Some crops like beans even put nitrogen back in to the soil.