Hi Gerry, 

Really this is up to you, once you have marked the bill as paid in QuickBooks then this posts the same as an expense transaction does, i.e to the selected expense account and the payment account. 

If you have many invoices and would find it easier to keep track of unpaid invoices in QuickBooks, then we'd suggest upgrading as there are reports for 'Unpaid Bills', which can be ordered by the due date, to give an easy overview. 

Let us know if you have any queries on this below!

Thanks