You can print a barcode from a computer just by formatting the text with the barcode font for the type of bar code you elect to use. And Filemaker can print that code to a label on either a sheet of labels in your printer or a dedicated lable printer.
The serial number can just be an auto-entered serial number field so that adding an item to your inventory just adds a new record and this field will automatically provide the unique serial number.
Here's a very recent link on using a barcode scanner with FileMaker Pro: Creating a new record/accessing a record upon scanning a barcode FileMaker Pro 11
You'll also want to visit and search the FM GO section of this forum where you can find some threads on using a barcode scanner with an iPhone--they don't function in exactly the same simple manner as the scanner connected to a computer if I recall correctly, so you'll want to talk with some people there who have actually set this up and used a scanner with such a device.