Wow, working on a Sat?!?! I hope you get some good time off to get the rest you need hun!
Funny you should ask @onedaymaybebaby! Of all things on my shopping list, I just checked off those today! I bought 3 flannelette and 3 muslins wraps today from Kmart, all 100% cotton (we were there for something else, but I thought I would pick them up anyway). I am renting too, but am lucky to have reverse cycle air in our main bedroom where we are going to place the bassinet for the first few months. That said, I am on the top floor and it's scorching hot in summer, so am not looking forward.
I think I am going to go for lightweight materials but might get 1 or 2 grosuits and 1 blanket that's a little warmer just in case. I read that babies tend to be overheated than not because parents tend to bundle them up. I will be buying singlets and short sleeved onesies mainly for start with and will see how we go.