Muslin:
The most commonly used fabric for wrapping is light weight muslin. While this is very cool, it's also the hardest fabric to wrap effectively with, as the loose weave seems to slip open as soon as baby wriggles. However in warmer climates and the middle of summer, muslin is often still the most appropriate. You can increase the effectiveness of musin by using a large wrap and buying good quality muslin swaddles.
Stretch cotton:
This is the easiest fabric to wrap securely with. Stretch cotton is suitable for use year-round and for babies of all sizes.
Flannelette:
This is suitable for the cooler months, as the brushed cotton is very snuggly feeling. However as flannelette is 100% cotton it can be used year round. It has very little stretch however, so it's best for newborn babies who are not very wriggly. Flannelette wraps are generally only 1m x 1m, so again only suitable for the first few months.
Merino:
This is perfect for swaddling newborns as it can help regulate your baby's temperature. However merino is stretchier than stretch cotton and can be hard to keep really firmly wrapped once babies are stronger and wriggler. A square merino wrap is really handy for a light blanket or pram blanket once you are no longer swaddling, so they are highly versatile.