Honestly, I would keep things as simple as possible in the beginning. As a first pass, put together a simple spreadsheet. When you find you have outgrown that (could take a while), I would recommend something like Freshbooks (https://www.freshbooks.com/pricing). I have been using Freshbooks as my invoicing/accounting software for several years now and have been quite pleased. However, I am starting to outgrow that platform and will likely transition to Quick Books in the near future.
I often find newer freelancers / small business owners fretting about which tools to use and wasting time looking for "the perfect tool." Remember that the goal of your tools is to save you time, and often the best tools are the simplest. While there is a SaaS product for everything, I nearly always start with a spreadsheet, and only when I truly outgrow the spreadsheet do I start looking for a better tool.