Howdy...
Yup... One more vote for PHP and MySQL to do the task... Can't think of any other combination except using ASP or CF rather than PHP... You got bunch of inventory items you have to display and update on the screen and I don't see that suitable for flat text file data... and to interact with the database, you will have to have server side script, as you might have suspected already, to do the job... ActionScript cannot handle that job alone... I wish it does, but...
I think there were a couple of Login system that goes with PHP and MySQL in FlashKit's tutorial section... You might want to go take a look at the file... Once you get that one going, you can add more inventory items onto the database and do the query with them to display/update into the Flash...
Let us know how it is coming along...