USB sticks are great for moving files around, and making temporary copies of things. USB sticks are not considered adequate for long term storage or real backups. Any 'found' external drive larger than your built-in drive can be used in a pinch, but it will quickly become annoying if it is too small.
Recommended size for an external drive for this purpose is larger than 2.5 times the size of what needs to be stored, for long term, trouble-free operation. Time machine (already built into your Mac) does its work at low propriety in the background, and does not get extra benefit from a drive that is fast.
Time machine works quietly and automatically in the background, without interrupting your regular work, and only saves the incremental changes (after the first full backup). Time machine backs up every connected drive that is in a Mac compatible format. it can not back up Windows format drives.
Time Machine's "claim to fame" is that it is the backup that gets done. It does not ruin performance of the rest of the computer while doing its backup operations. You do not have to set aside a "Special Time" when you only do backups. When you need it, your Time machine Backup is much more likely to be there.
How to use Time Machine to Backup or Restore your Mac:
Back up your Mac with Time Machine - Apple Support
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