Filing systems in payables are usually designed around how documents are stored and should be designed around how they are retrieved. Nobody ever needs to admire the structure. They need to find one invoice, months later, knowing one of four things about it, and a system that supports only one of the four will fail three quarters of the time.
The four ways people search
By supplier, by invoice number, by amount, and by roughly when it was paid. A filing structure organised by supplier and month supports the first and the last well and the middle two badly. Digital records support all four naturally, which is the single biggest practical advantage of moving off paper, ahead of any saving in effort.
What to store with the document
The received date, the purchase order reference, the match result, the approval with its date and approver, the coding, and the payment date. Those turn a stored image into a record that answers questions on its own, without somebody having to reconstruct the story from three systems and a memory.
Retention, decided deliberately
How long invoices and their approval history must be kept depends on your jurisdiction and tax position, and it is worth writing down rather than defaulting to keeping everything forever or clearing space when it runs out. Whatever you decide, keep the approval trail with the invoice: it is part of the record of the transaction, not an administrative extra.
Questions people ask about accounts payable filing system
Should we file by supplier or by date?
For digital records the question mostly disappears, since you can search either way. For paper, by month within supplier is the usual compromise.
How long should we keep invoices?
According to your own retention obligations, which vary by jurisdiction and tax position. Decide it as a policy and apply it consistently.
Do we need the paper if we have a scan?
Usually not once you are confident the scan is complete and legible, subject to your own obligations. Make that a documented decision rather than an assumption.