The Saiya-Jin mainly wear armour. There are several armour shops in all cities where a Saiya-Jin can upgrade the armour or replace it.
The quality of their armour is so good, that customers from all over the universe come to get one of these Saiya-Jin armour, making this a very well-running business.
Younger children usually don't wear armour, but animal skins or just some rags. The Saiya-Jin don't really see nudity as innapropriate so often enough, children run around being naked.