Cost of Goods Sold and Sales of Product Income: What if I don't keep inventory, but purchase things for resale, will I use Cost of Goods Sold and Sales of Product Income?

You marked this as QBO and QBSE

what you name the income account is up to you, as long as sales post to an income type account

In QBO you would use the periodic inventory system.  There are two ways to do periodic inventory, choose one and stick with it, you can not mix and match

1. (my preference) Create an asset account called purchases and post all purchases of item for resale to that account.  Periodically, weekly, monthly, etc value the inventory on hand, subtract that value from the amount shown in the purchases account and do a journal entry for the answer to the subtraction
debit COGS for that value
credit purchases for that value

OR

2.  Post all purchases to COGS.  Periodically, but at least at the end of the year, you value the inventory on hand and do a journal entry.
debit the asset purchases account for that value
credit COGS for that value

Print the P&L
then reverse the journal entry
debit COGS for that same value
credit the asset purchases account for that value

This last journal entry, moves the value of what was on hand at the end of year back to COGS so the cost will be counted against the new year sales.