So you want to run Linux on USB stick. Because your laptop system is in a mess, or because you are borrowing your daughter's machine, or just because it's fun. Whatever reason, it's worth the trouble.
For Linux distribution you choose Xubuntu, because it's light enough and pretty. For a USB stick you choose just a stick. Mine is 4 GB, USB 2.0. Of course 3.0 would be faster.
In your Linux computer go to Synaptics an install unetbootin. You could also simply use Start Up Disk Creator, but that doesn't allow going for persistence any more. But with unetbootin you can get a persistent stick system with a few steps.
linux /casper/vmlinuz.efi persistent file=/cdrom/preseed/xubuntu.seed boot=casper quiet splash ---
And so you are ready. Boot with your USB stick and create a new user by your name. Logout from test user and login with your new account.