I'm not sure quite what you want to know, but here goes:
This is an A-5, or Auto-5 semi-automatic shotgun.
Your gun was made in 1960, and was the 58,448th gun made in that year. It is a "Sweet Sixteen," which means that it was specifically made to only chamber 2.75" shells (not 3") and is 10oz. lighter than a standard sixteen gauge A-5. This information was derived from your serial number.
Because your gun was made before 1967, it is likely to have a round knob rather than a flat knob (you didn't specify). Also, because your gun was made in 1960 (and the buttplate is a dead giveaway), it was manufactured by Fabrique National in Belguim, hence the FN. FN quit making this gun in 1975, and in 1987 this model began to be manufactured in Japan.
The barrel is likely actually a 26" or 28", because those are the actual measurements that Browning manufactured (also a 30"). The choke is fixed, and the barrel will have one or more stars engraved on it near the muzzle that you can use to identify what choke it is (in the "Browning choke codes" listed at the top of the Browning forum). Finally, the St. Louis & Montreal address on the barrel indicates that it was manufactured between 1959 - 1968. Thus, this is possibly the original barrel to the gun as well (likely, if your grandfather was the original owner).
If you need to know the value of the gun, it's $2. I can send you a check....
Actually, my grandfather has a gun almost just like this, only manufactured in 1961 and I have just purchased an A-5 "Light Twelve" that was made in '64. I did my research before buying, so that's the benefit you're getting here. Most of this stuff can be found from this site and Browning's website here:
http://www.browning.com/services/dategu ... .asp?id=13
If you really need to know the value, you'll have to ask someone who has a bluebook of gun values. I wrote down the values of the Sweet Sixteens for my use, but only wrote down the numbers for the vent-rib model. The vent-rib books slightly higher than a solid-rib model.
Hope I was of some help.