What do you think about me asking my landlord to buy some furniture for us?
Why would you ask your landlord to purchase something for you?
We have been pretty well with her. And she likes to give us good things for free
Getting things bought for you is cool, but most people wouldn't expect a landlord to make such large purchases like furniture and that would be expected for you to buy yourself.  They might get upset with you if you're asking for something so large.
Your not a real person are you?
I know a lot of people and they would say that you should just be grateful for what you do receive. You should speak with your landlord and ask what they're willing to buy, but not push it or else they may become annoyed.