The mulch being used now will make a difference in the
soil for a long time.
What mulch is best depends on what you are planting and what you want out of it. For a garden that is focusing on plants native to Utah you want to use rocks. They can be cheap, are what the plants are used to, and can be very ornamental. For a food producing garden you will find rocks to be lacking.
For vegetables I want something with few weed seeds and is biodegradable, readily available, and will improve my soil long term. While there are many materials that fit the first three conditions, there is only one material that I know of that readily meets the last: wood.
As I write this I have this nagging feeling that some of you are picturing a garden filled with cut lumber laid out like a wood floor. While this would work, there are better ways that I will cover later in this post.
The things that make wood so special are the complex chemicals that take a long time to break down. These chemicals are usually polyphenols and particularly lignin. As these chemicals break down they are a major contribution to humic acid, a class of organic chemicals that improve almost all soils.
Once the humic acid is developed, it lasts a long time. In fact if you mulch regularly for ten years you will make a 1,000 year difference in the soil--if you do it right!
The most important thing to do to get this 1,000 year effect is to not till. Tilling speeds up the decomposition to the point where it starts interfering with the creation of humic acid. You have to put the wood on top and leave it there!
Some suppliers sell a fossilized organic product mined near the coal fields here in the west. It has some potential value, but for the creation of long term good soil it has not been proven or disproven. It also costs more than creating your own humic acid through mulching.
Also, be aware that adding just wood products may throw your soil chemistry out of sink. Please see my post on Sheet Mulching for more information.
As for what kind of wood to use, slow growing woods are best. Oak, hickory, cherry, fir, pine, and many others are all very good. You can use saw dust, chipped trees, large wood chunks, or whatever is cheap and available in your area. Just be careful of paint, glue, and any chemical additives. They may be toxic for you or your plants.
Have fun and let me know how things work.