A broad question that can be quite complex.
The RE adopted a new uniform in 1933. The uniformi metropolitane was a wool, open collar, four pocket, with a waist belt, and pantaloni that only extended to the knee with puttees. It was g-v color and underwent several modifications that only changed some details, but no major revisions to the basic design. Unless authorized to wear the uniformi coloniale, everyone wore the uniformi metropolitane. Google Italian WW2 uniforms.
The uniformi coloniale was similar in cut, made from khaki colored cotton and lacked the waist belt. It was authorized in AS and the AOI.
Mixing uniforms in the AS was common as new troops arriving in AS didn't always have the uniform coloniale issued before they departed Italy. The desert can get cold, and wool does insulate a person from the heat, so the wool uniform was not necessarily a bad uniform. By the time the war gets to Tunisia, the uniformi metropolitane was common.
The Osprey books are a good start. Note that the RE has some specialist uniforms (paratroopers, tankers, alpini, and ski troops afre some examples), and their were many small differences in some uniforms and equipment. The USSME (Italian historical office) has many books on uniforms because there are many differences to the basic uniform.
