I bought 3 baby blankets and about 10 bunny rugs (flanno), and 3 muslin squares and no actual wraps. My bub was in a sleeping bag by 2 weeks as he was a big kicker so you might like to get one of those too. The bunny rugs are good for all sorts of things including being used as chuck rags. I got my bunny rugs from Safeway or Coles, the blankets & muslin squares at Ikea.

I'd suggest getting around 4 or 5 Bonds type wondersuits with the mittens in them. If you buy the bonds ones go for 000 if you get another brand buy a combination of 000 & 0000. Even if the weather is hot bubs could well be sleeping in them at night, depending on how low the temp gets overnight.

Get a few cotton long sleeved jump suits, short sleeved jump suits and a couple that don't have arms in them. You can get these really cheap at Best & Less so it doesn't have to cost you much to get a variety. If you team them with long pants you can cover a variety of temperatures for the Melbourne weather. You can get singlets as well, but I tend to use the short sleeved or no sleeved legless jump suits as a singlet as they don't ride up. If you get Bonds singlets get 000 other brands 0000.

Cotton is better for rashy bubs, so if you think your bub might be prone to that type of thing avoid the wondersuits. I have just got rid of everything that is not 100% cotton due to this issue. I didn't expect to have to do that.

Get a pack of Bonds Stay on Socks. Don't bother with any other type of sock cos they don't stay on. These ones do. A pack of 3 will do to get started with. Bubs will sometimes still wear socks even when it's warm cos they can get cold feet even if the rest of them is warm.

Don't worry about the play swing/gym for now - plenty of time to worry about that later on.

Make sure you get bibs & facewashers.

Don't bother with all the scented baby oils & lotions as you'll be advised to only use olive oil.

Get a thermometer for the bath. It's really hard to work out if it's the correct temp otherwise.

Towel wrap for after the bath.

Something musical to help bubs sleep. We have a leap tad that plays 5 or ten minutes music to help settle him. It works wonders.