I may be misunderstanding, you used to be able to plug the two devices together over firewire and transfer directly. You can't EASILY do that any longer using USB3. Not sure if that's what you were referring to. I believe technically it's still possible with the right cables though - see this link:
https://www.macworld.com/article/29...-the-right-cable-which-apple-doesnt-sell.html
Appears it's Target Disk Mode only, not Migration Assistant though.
So you can use external HDD. If you can borrow one, that's great. But your USB3 drive will plug into your old device natively, though to plug into the new MBPro it will need a USB-A to USB-C adaptor.
But if you're buying an external drive it might also be worth getting an external SSD, since that will be far faster. You're going to want a backup strategy of some kind (what do you do today?) so if you're starting fresh, maybe the extra money on an external SSD is a better option?
This is a USB-C SSD that comes with a USB-A plug.
https://www.amazon.com/LaCie-Rugged...1534447122&sr=8-4&keywords=external+ssd+usb-c
So longer term that's perhaps a better option. Or buy a USB3 drive and for future use just use an adaptor for USB-C. USB-C adaptors sometimes bring complications because USB3 leaks 2.4GHz frequency that can kill your wifi if your wifi is also 2.4GHz.
So assuming that you don't have a backup strategy, I'd get a USB-C SSD that is backwards compatible with USB3/USB-A, rather than a traditional spinning platter USB3 drive and fuss with an adaptor for future use.
If you're sorted for backups already then the cheapest option is a cable like mentioned in the first link and TDM. I don't have experience with that cable but I'm sure there are folks here that do. It sounds limiting though.
When I migrate, I use a USB drive, or use Wifi from my Time Machine backup on my NAS (slow!).