There are basically three different types of insulation material:
1. Organic - those derived from natural vegetation or similar renewable sources, which tend to require a low energy use in manufacture (a low ‘embodied energy’). Examples are sheep’s wool, cellulose, cork, wood fibre, and hemp.
2. Inorganic - derived from naturally occurring minerals which are non-renewable but plentiful at source. Likely to have a higher embodied energy than organic materials. Examples are mineral/glass fibre, perlite and vermiculite (from volcanic rock) and rigid foamed glass.
3. Fossil organic - derived by chemical processes from fossilised vegetation (oil) - a finite resource. Fossil organic insulation materials such as expanded polystyrene and polyisocyanurate or phenolic foam are highly processed, resulting in a high embodied energy.
Which is best? If possible it is better to choose insulation materials that have not been heavily processed as this will reduce the carbon footprint and environmental impact of your home. But it is far better to install cheaper inorganic or fossil organic materials with the right physical properties and a low thermal conductivity than to install nothing at all.
In many cases, organic insulation material can be applied instead of inorganic or fossil organic, but there are exceptions. For example, there is not yet an organic insulation material suitable for cavity wall insulation.
Think also about the ease of installation. Loose fill insulation is quick to put in in lofts, but cannot be DIY installed in anything other than a flat place. Rigid boards and batts will come in certain sizes, but need to be cut to shape if you have some unusual spaces. Some materials can be cut with a knife, but a few will need a saw. Some mineral wool now comes in a thin foil or plastic wrap, to protect from the fibres. You should still wear a face mask when installing any type of installation, as small fibres of any kind are best not inhaled.