There are a number of great options for creating a walking trail or nature path. If you want to go with a crushed stone pathway, you can order either decomposed granite (which is basically a bit larger than sand), or you can go with screening which is a bit larger, but also crushed stone. If you're looking to build a path out of mulch or wood chips, then basically any type will work. If you're going to be building a wood chip path, you should check to make sure that there is not arsenic in the wood because some decorative mulch does use arsenic.
Here are some other great resources:
http://www.rd.com/your-home/yard-and-garden/landscaping/crushed-stone-path/article27144.html
http://www.dummies.com/WileyCDA/DummiesArticle/Adding-Paths-to-Your-Landscape.id-2942.html
I've done a few walking paths for parents/adults to use while the kids play on the playground. Typically we have used a skid loader with a bucket on the front to take the top layer of grass, sod, or dirt off (which can be used elsewhere if done well). You can also use flat shovels (but this will take much longer and require more arm and back muscle). I've taken it down 4" or so and made it approximately 4.5' wide.
Once that is done, you can add any edging you prefer. I've done both brick edging as well as landscape timbers and rebar (your choice). There are many other options though. It's a good idea to put down a roll of weed block (you'll be glad you did). Then, in the past I've used playground safety surfacing such as Engineered Wood Fiber, which is ADA accessible once compacted a bit. However, as was mentioned above other materials will work too. Just remember to double check that it meets the ADA standards.
In addition to putting down the surfacing for the walking trail, it's also a fun idea to place signs or pictures along the path that highlight some of the natural vegetation in the area or the distance traveled. It's a good way to keep both kids and adults engaged. This can be anything from a simple sign that says the type of tree they are walking past to the type of surfacing they are walking on or the distance until they reach the playground or park.
If you decide to use crushed rock for your walking path, make sure that you double check how much you will need to order. I once ordered two tons for a walking path I was doing, thinking that would be enough, and then we wound up ordering 10 extra tons. So check with the company that will be selling you the rock and ask them what they think will cover your area. You don't want to wind up paying a delivery charge twice for extra materials! Good luck!