Welcome to the community! QuickBooks Online is a great tool for keeping track of your expenses, as it lets you easily keep a detailed record of separate under your various suppliers. Each expense is considered as an individual transaction with its own underlying journal entry. They will be categorized based on the selected Payee, Payment account and Category. I'll be happy to help you get started with this.
Since it sounds like you've already set up your payee, setting up you chart of accounts is the best way to further categorize your expenses. You can add a new account in a few simple steps to select it on an expense:
Select Accounting from the left menu.
Click New.
Select the appropriate account type in the Category Type drop down menu.
Select the appropriate Detail Type in the drop down menu.
Fill in all remaining fields and click Save and Close.