The mansion had so many bedrooms and a lot of furniture was needed which wasn't a joke. She wanted every room to be different and unique and have a story behind it, and she has time, although it was limited but it was still there.
So, she first started with her own wing which was quite easy as she knows herself at least better than everyone.
Alita didn't have a favorite color perse but she was someone who loves vibrant colors as they somehow brighten her world. She had been seeing a lot of black and white lately, she was about to go nuts.
In the end, she chose some maroon and cherry for her room, although this can change with time. Alita began to design her own furniture as she was planning on having those ancient carpenters make it for her.