This needs to be started on a running system and you follow the instruction. You choose "Create installation media" and you select your USB Key as the target and you create the installation media like that.
You cannot just download the tool and put it on the usb key. It will not work. You have to run the tool and follow the steps.
At which time Drive such and such will probably be less expensive than it is today. Or more options will appear, some of which are 'faster', at the same price.
Storage space costs across all types are on a continual march downwards.