Changi airport (Singapore) is indeed excellent for a stopover if you fly Singapore Airlines - they have the most beautiful rest areas with orchids and koi ................ really attractive and if you have more than 6 hours there is time to go into the City and sample a cocktail on the verandah...
Spring or autumn are best in terms of cost and, arguably, weather.
Depending on how long you plan to stay is what you can do - sense says don't try to do too much but when there is only one chance to see places, sense goes out the window!
We have been to WA a few times staying with relatives...