Best file system for USB stick for backup purposes
From Apple KB : Backup disks you can use with Time Machine 


  Formatting a backup disk for use with Time Machine
  
  The most common format for a Time Machine backup disk is Mac OS Extended (Journaled) format. 
  
  Time Machine also supports Mac OS Extended (Case-sensitive, Journaled), Mac OS Extended (Case-sensitive, Journaled, Encrypted), and Xsan formats.
  If your disk uses the Master Boot Record (MBR) partition type, some partitions might not be available for use with Time Machine.


In short, use a Journaled HFS+ partition on a GUID[GPT] formatted disk for best results.