The choice of which fibre to use for your project is completely dependent on personal preference.
Cotton and Wool are natural fibres and are usually sold as blends or pure products. Polyester and Acrylic are made from synthetic fibres. Cotton: Cotton is soft breathable and great for summertime, baby items (i.e dolls & amigurumi) and dishcloths. Cotton is easily stretched and has a heavier feel to it. Wool: Wool requires more care with washing and care and some people find it itchy.
However, wool is also warm, insulating, and elastic. It's perfect for those cool/cold months and is odour resistant. Polyester: Polyester is not as soft or breathable as natural fibres it is however, strong, durable and often blended with other fibres ie. cotton. Its seen as a good fibre to use with items that need to be hardwearing i.e bags.
Acrylic: Acrylic yarn is cheap, durable, machine washable and lightweight. Acrylic fibres these days can be very soft and are used to make a variety of garments and projects. Those new to knitting and crochet are often guided to use acrylic to begin with before moving to more expensive fibres.