Firmness is the single most important spec, full stop — a soft mattress increases suffocation risk for young babies, so cot mattresses are deliberately much firmer than adult ones. Never substitute a soft mattress or extra padding for a baby under one.
Foam mattresses are lightweight and budget-friendly; sprung mattresses tend to offer more airflow and can last through several children in better condition; coir (natural fibre) mattresses are firm and breathable but usually cost more.
Whichever material you choose, the mattress needs to fit the cot with no gaps around the edges — a gap large enough to trap a limb or head is a genuine hazard, so always check exact dimensions against your specific cot, not just the general size category.