Go straight for international certifications that guarantee environmental respect throughout the entire supply chain, not just the raw material. GOTS for organic wool is the most reliable standard, but OEKO-TEX and EU Ecolabel also give you concrete guarantees on dyes and processes. As others have already mentioned, greenwashing is rampant in this sector, so it's better to rely on verifiable labels than on marketing slogans.
In Italy you'll find some small producers that do good work. Brands like Lana Grossa have fairly transparent organic lines, and then there are smaller weavers selling online who really specify where everything is made. Try searching through Italian yarn e-commerce sites or contact some mills directly that offer complete traceability. It costs more than conventional yarn, but at least you know where your money's going.
As for recycled versus organic, it really depends on what you can afford and how much weight you give to the details. Regenerated yarn reuses material that would otherwise end up as waste, which is interesting from a circular perspective, but virgin organic still remains the cleanest choice if grown according to serious standards. The most important thing is to avoid that stuff that says eco but uses toxic dyes - always check the chemical composition of the processes, don't just stop at "organic" on the package.