Fast growth is the usual reason people buy a tree, and it comes with a trade-off worth knowing about. The quickest species are generally shorter-lived and have softer timber, which makes them better as a nurse crop than a permanent feature.
Wattles, alders and poplars will deliver height within two or three years but may need replacing within twenty. Lilly pilly, pittosporum and photinia grow nearly as fast as a screen and last considerably longer.
Buying an advanced size is often faster than buying a fast-growing species. A 200L tree starts years ahead of a 45L, whatever the growth rate on the label.