Straw work great. Check craigslist.. usually you can score them for $5 a bale or less. Or your localfeed store. Another good resource are tree trimmers in your area. Call em up and tell them they are welcome to drop a load of shredded trees at your place every once in a while.. Usually they will be more than happy to as it can save them a trip to the dump.. Happy growing!
I don’t mean to discourage you, but I would instead encourage you to get the soil test. Nearly every gardening book starts with that. I didn’t do that and I regret it.
The soil test will tell you how to better balance your nutrients via mineral amendments. Just mulching-mulching-mulching doesn’t seem to do much for nutrient balancing and in fact can exacerbate nutrient deficiencies.
After 3 years of having made mulching my religion, I can tell you that it did not work miracles for me. It helped, but there is more to the story then just adding organic matter.
That being said, If you can get your hands on chipped wood, it will go farther than anything else in your garden. Whereas everything else will evaporate before your eyes, wood chips stick around at least 6-8 months and do a lot to create the loose soil texture gardeners like. People have built a garden with only wood chip ammendments and they seem to be doing well (google: back to eden wood chips).
I got big bales of straw and I add it sparingly to the top to keep humidity in and shade the soil. In the second year of no-till gardening weeds are much less of a pain, so the amount of mulching is going down.
You can also mulch with very well-done compost (looks like potting soil) if you can get enough of it to keep applying. Grass is a bad mulching material. Hay is likewise bad, much worse than straw in my opinion. I don’t get wheat growing in my beds very much, but hay grass did grow excessively. Leaves are good if shreaded or spread thinly enough that they won’t create a barrier to rain.