I can't think of any reason not to put wood chips on the trails and have never heard of any downsides, except that wood in the soil competes with plants for nutrients - but that's usually cited as a reason not to use it in combination with potting soil vs. a trail where you don't want plants to grow.

I would say the most common species would be those that are sawn for lumber in the area. And that would be either Douglas-fir or a combination of western hemlock and a true fir like grand fir. Sawmills produce the chips as a byproduct of producing lumber from round logs (i.e., byproducts are unavoidable!).

However, I doubt you'd be able to purchase directly from a sawmill since they sell in truckload quantities to businesses like pulp mills. So you could simply look for businesses selling mulch, chips, gravel, etc. in your area or contact a tree service company since they will often have lots of chipped material from downed trees, trimmings, etc.