Is your wall a retaining one (weeping plants good for this type of wall) or free standing(vining plants good for this)? What kind of sun exposure does does the face of the wall that you want to cover have? What growing zone does your location have? Not giving a specific location forces one to consider a whole continent with varied climate. Also, the answer might be a bit hard to get because your location is Australia and there is a bit more unfamiliarity of GOY members with this part of the garden world and their desire is to give you the best answer possible. My personal suggestion would be to inquire at your local garden center.

'Like ivy but not Ivy' - Fatshedera comes to mind. A cross between Fatsia japonica and Hedera (Ivy). Very well behaved.

Have you looked at gardens around where you live? You can see which ones will do well. In the UK it makes a difference which way the wall faces, ie will the plant be in full sun or in shade? It will also make a difference accoding to how tall and long the area you want to cover is.

And how tall is the wall?