I just started in the pizza business but my other business is as a QuickBooks Consultant. The best approach is to use a sales receipt. You would want to set up non-inventory items for the categories that appear on your Z out report. You would enter a sales receipt for each day of sales based on the Z out. The goal of the exercise is to record all of the income and then to record how the income was received i.e. cash, credit etc. Once you have the income items setup you will also need to set up payment type items. You will want to pick the appropriate payment method for each payment type item. Your cash item should be deposited to a Cash in Drawer account (bank account type). Credit cards and checks if you take them should be deposited to Undeposited Funds. You will then need to go to the Make Deposits window and deposit those items into batches the way they were deposited into your bank account.
Once you have setup all of your non-inventory items for your categories and your payment items, you will want to build a sales receipt that you will memorize. That way you only have to do this exercise one time and from then on you go to the memorized transaction and just change the numbers. The setup should be all of the non-inventory income will be the first lines of the sales receipt, then you will list the payment items and put amounts in them that are negative. The goal of the whole exercise is to have a sales receipt that shows zero at the bottom. The other thing you will have to watch for in the setup is which items are taxable vs non-taxable since QuickBooks will calculate the tax for you. Hope that helps.