The flat file version of dbman can handle a db up to about 1 mb in size. If you anticipate having thousands of users and/or files then the SQL version would be better suited for you (or maybe gossamer-links?).
Both versions are highly customizable. There are also lots of people who can modify the program for you, for pay.
You can set dbman so that users can view only their records (links to file downloads).
I'd suggest starting with the flat file version and add the the following mods:
Notify Admin of New Users
See also www.redundantcartridge.com/dbman for the "unofficial FAQ" maintained by LoisC. There you will find tons of mods/hacks for dbman flat file. It just depends upon your comfort level with Perl and HTML.
Many of the dbman users had no prior Perl knowledge before modifying the script and have learned by a hands on method.