It was envisaged that South Australia would be a self-supporting 'province'. Founded as an experiment in 'systematic colonisation' based on a plan devised by Edward Gibbon Wakefield and Robert Gouger, land in the colony was sold rather than given away and the money raised used to funded free immigration for 'worthy' labourers and their families.
The first land purchasers were either middle class families seeking religious freedom or simply better opportunities, or absentee speculators who quickly drove up land values.
The majority of those who came to South Australia in the 19th century were economic migrants - a situation which continued through the 20th century.
A small number were German and Polish religious and intellectual refugees from Prussia.
Illustration from the training manual, The Log of a Merchant Officer (1854)
Search like a librarian:
Remember that photography did not begin until the 1850s but before this date a painting or drawing of the ship may exist.
The State Library has two major collections of ships images: the AD Edwardes Collection (19th century) and the Arbon/Le Maistre Collection (20th century).
You can search in the catalogue for photographs of the ship your family arrived in by the name of the ship. The best approach is to do a keyword search. For example, for images of the HMS Buffalo type: 'buffalo ship'.
Listen to Professor Angela Woollacott discuss the growth of the settler society in Australia (includes a 12 minute introduction to the History Council of SA).