I have a settled on Toggl for time tracking and Zoho Books for invoicing. Toggl supports csv export and Zoho Books has an import feature that makes getting data from one to the next fairly simple, with the help of a simple script I wrote to transform the data (https://github.com/joshrickert/toggl-zoho-books-timesheet-co...).

I did a pretty exhaustive search when I set out to solve this problem a couple years ago, and ended up with a considerable amount of research that I summarized on my blog (https://joshrickert.com/blog/invoicing-apps-for-freelancers/).