You don't need to be an accountant to keep clean books as a freelancer. At its core, DIY bookkeeping comes down to three habits done consistently: log every invoice you send, log every expense as it happens (not in a batch at tax time), and reconcile against your bank statement monthly so nothing slips through.
Start by separating business and personal finances, even a basic separate checking account makes tracking dramatically easier and is often required to maintain LLC liability protection. From there, a simple system of an invoice generator plus an expense tracker covers most of what a freelancer actually needs day to day, without the overhead of full accounting software built for businesses with employees and inventory.
Set a recurring 20-30 minute block once a week to log expenses and check on unpaid invoices, this single habit prevents the year-end scramble more than any tool choice does. When it's time for taxes, a clean log of income and categorized expenses is 90% of what your accountant or tax software needs.