Insulation can contribute to the sustainability of a home both by being sustainably-sourced and by reducing heating and cooling requirements. The longer the insulation lasts, the greater its contribution to your home's sustainability. It is also important to select insulation that can be installed easily, without tearing out walls and producing unnecessary waste.
Here are some factors to consider:
Are you building a new home or simply upgrading an existing house? It simply isn't practical to re-do an existing home with straw-bale walls, but you can easily fill an attic with fiberglass, cellulose, denim, or other loose insulation.
Continuing from that, the type of building material used is also a major factor. You can't put loose-fill cellulose in a poured concrete wall, but you can use insulating concrete forms or foam boards. Wood houses have a lot of cavities that make blown-in insulation an attractive option, especially for retrofits. Filling empty cavities with cellulose or fiberglass is a fairly non-invasive strategy for wood structures as it only requires you to drill holes in the wall then plug them again. But if you are already re-siding the house, foam boards under the new siding might be an attractive option.
Sunlight damages most insulating foams.
Humidity can damage many types of insulation, and your choice of insulation will affect (or depend on) your strategies for dealing with moisture produced in the home or entering from outside.
Mice are happy to nest in fiberglass, as reported on the DIY/Home Improvement sister site.
Straw bale construction works well if you can find a contractor in your area familiar with it or if you have the skills to do it yourself.
Wool insulation (mentioned in the question) is sustainable if wool is produced in excess near the house in question. If you would have to make special arrangements to have it shipped from a far away place, you should consider other options.