Tracking the Processing of New Members
if you are wanting to track who was sent something, then I would create a new Activity Type for 'send member pack' and then via a Search  you would be able to add an Activity to any member that you are sending the pack to, and set it to Completed, and hence you know the job has been done.

NOTE: when adding an Activity to lots of contacts via Actions on the Search screen there is a small checkbox that lets you specify whether you are making one Activity that relates to LOTS of contacts, or one Activity for EACH contact. You are welcome to choose, but i would suggest doing the latter option, so you have a single Activity record for each Member.

EDIT: (per frTommy suggestion) You could automate this somewhat by utilizing CiviRules to Schedule an Activity of "Send Member Pack" whenever a Membership is added