Value is too difficult to be accurate without seeing the gun. Condition which includes the amount of original finish and original configuration will determine value. Recommend taking it to a gun shop for appraisal.
What is the value of a 12 gauge Browning shotgun serial J68824?
0-250 USD depending on condition.
1000 USD
$350
Basically impossible to value a weapon with just the gauge and sn.
If you mean a Browning B-2000 12 gauge shotgun then the value would be 495 dollars for a shotgun in the condition you describe.
Browning never made a Model 51 shotgun.
Not a valid Browning serial number.
You will have to call Browning with the serial number to find out.
http://www.browning.com/products
Use the link below
100-1000 usd