Generating unique file names

[matte]

   I am doing a simple [1]backup Bash script that creates a backup archive of a
   folder (or file) I am working on. I want to have snapshaps all saved to one
   directory. To ensure unique name, I am currently appending the date and time
   to "MyArcName_data_time." But this creates a long and ugly name. I'd like
   either something cleaner like a unique number appended (based on total files
   in directory), or some random temp filename generator function that I don't
   yet know about.

   The count would be sufficient, as each folder will always hold ONLY these
   archives, and no hidden files.
   Thus, my directory would be:
   myArcName_1.tar.gz
   myArcName_2.tar.gz
   myArcName_3.tar.gz
   ...
   iF there's some bash function for this, groovy. If not, i just need to know
   how to count the directories from inside my script.
   Thanks in advance

References

   1. http://www.linuxforums.org/forum/