This sounds really cool what you are doing, and I am definitely interested. The timeline once the contract is signed, is typically 2-4 weeks. This is affected by how much your budget is. I am usually able to negotiate how many revisions, and how many different logo concepts I will finalize based on your budget.
If you need me to clarify anything just let me know.
もし確認することがあれば、お知らせください。