Instead of a memory stick (which gets pricey fast)....they make external hard drives, very often used as backup drives. They have, say, a Terra-byte of storage (1000 GB) on them and are attached by USB and sell for about $100.00. Just don't move em around when they are "on".
The memory stick (USB Flash Drive) is a more-robust choice...but a lot more expensive for a decent capacity.
Of course, since you're just backing up your "old" system, you can probably just get a smaller drive, not worry about speed, and when done....just have a spare flash drive around. That works too.
Kinda all depends on your answer to the questions: "What happens to the flash drive when all this is over? How will I back up my NEW system?"