34 gauge/ 0.16mm good to start with but its not very strong.
28 gauge/ 0.32mm (usually printed 0.3mm) is the most popular. Comes in lots of colours. This gauge is nice to work with and produces a firmer finished work. Good with lightweight beads too.
20 gauge/ 0.81 (usually printed 0.8mm) is good for pendants, charms, items with heavy beads (crystal, glass). Be careful of your fingers with this size it can cut into them.
16 + gauge/ 1.29mm (usually printed 1.3mm) not used to crochet with but for making supports and shapes to crochet on. Also for making findings (earring wires, clasps)