If you need a basic tool (well actually not basic but you will see it as a basic tool because of the User Interface), Trello is a good start. I've been using Trello since 2013. You're talking about Freelancing so I think the most important thing here are:
1. You might have more contracts. So create one board for one contract.
2. In each board, create a column for General Information such as: Contract, Document, Requirements, Invoice, Receipt.
3. The 2nd column might be Deals from Customers. Here you can refine the requirements and what to do for them.
4. The 3rd column is To Do. Clearly, you put your tasks here. Each main task is a Trello Card. Sub-tasks are your Checklist Items.
5. The 4th is In Progress column. Drag your Cards from To Do column to this column to know your current status.
6. Last one will be Done column. I don't need to explain more in this column.
During the work you need to use Trello Labels to high light your important stuff. You can search your works easily by filtering these labels during the time.
Hope this can help. And good luck with your freelancing career!