Can anyone give me recommendations on where to purchase relatively cheap groceries?
I am unfamiliar with Australian stores so I am unsure of which ones are considered cheap, high-quality, or organic, etc.
If you are looking for frozen foods, vegetables and other household items, then Laguna Oriental and Hometown Asian Supermarket is best. And if you are a cheese lover then go to Spring Street Grocer in Melbourne.
Fresh produce and even some pastas, markets, queen vic in the city, preston, south melb, footscray or farmers markets. If you eat meat, I would recommend finding your local butcher, higher quality, better prices.
Aldi is ok, I'm not 100% sold that it's THAT much cheaper. Their fresh produce isn't great ie. Fruit veg and meats. Shelf and freezer is alright though.
Cleaning products it depends on how picky you are, reject shop stocks a lot of decent stuff in terms of cleaning for bathroom kitchen and laundry if you're on a tight budget.