If you purchase PSE 2020 it will come with its own serial number. The upgrade pricing is a discount for users of previous versions but shop around as on-line stores will sometimes offer the full version at an even lower price. Buy whichever is the cheapest. If you go for the upgrade and install it on a new computer you will need both the new and old serial numbers.
Bear in mind that Adobe usually releases a new update in late September/early October. So you may wish to wait unless PSE 2020 gets substantially reduced in price in anticipation. You could download the 30 day free trial now.