I use a bit of Trello and Freedcamp for my todos and planning.
I also use RescueTime to make sure I'm keeping productive. I'm actually exploring adding integrations with RescueTime with LogMyHours, to see how productive you were for each timesheet, and reporting period.
I would 100% recommend you do _not_ use a spreadsheet or make your own software for this. Invoices are just far too important. Screwing up your time sheets, invoicing twice or forgetting to invoice would be horrendous. Harvest is only around $100 a year when you need the paid plan (it's always free for around 2 ongoing clients I think, the option is a little hidden). It might look simple enough that you could get away with a simple spreadsheet for example but Harvest makes it much harder to make mistakes (Did you put something in the wrong cell? Did you remember to mark an invoice as sent? Paid?) and a single mistake can be costly.
