I thin most people have given you GREAT ideas on things to buy, just remember at the start it doesn't need to be new, when i first moved out i was 18 and NOTHING matched in my house, i bought things from the op shop (furniture etc) and had family give me things they didn't need anymore.

Another great thing is tell family & friends your planning on moving, for your b'day etc they can pool together and get something you NEED or even give you cash.

Stay true to yourself hun and i know you can do it, you and Grace will have an amazing time in your own place with your own space.. start small and work your way up.
You have the determination and i know you will make it work.

Re sharing, i had the WORST experience with someone i thought i could trust, i worked days and she worked nights and i THOUGHT she was paying the rent during the day, problem was she wasn't and she was hiding the letters about it.
I was lucky as a friend of mine owned the house i was renting, i kicked out the other friend and my friend wrote off the debt and we started fresh.
Just make sure you have set boundaries and that you think you CAN live with this person 24/7.

I know you can do it!