First the Remington 3200 is not the forerunner of the K32. The K32 was derived from the Remington 32.
The 3200 is a fine gun that will last for a lifetime or two. They are well made and have one of the best triggers you will find in any double.
One thing to check is whether the gun has had the factory modification. This is indicated by a dot in the serial number and small screws next to the hole in the breech face the firing pins protrude through when you pull the trigger. Ask the owner if this has been done, if he is honest about it he will tell you.
The 3200 has one achillies heel, it is the forend "Iron". This is the metal plate in the forend that holds the forend to the gun. It also is part of the cocking and ejecting mechanism. Because it is a sheet stamping it will flex a bit. This can cause the forend wood to crack. This is a well known fault in the 3200 design and probably caused Remington to drop the gun as they were constantly replacing forends. Many high volume shooters disconnected the ejectors and this usually solved the problem. Almost all doubles use a casting or forging for the forend iron.
That said the 3200 is a great gun, albeit a bit on the heavy side. Unfortunately they were produced before the interchangeable choke tube revolution and the barrel setup makes it difficult to retrofit tubes. Briley has thin walled tubes that can be fitted however.
As to price, the book lists the price for a 100% gun at $1250. Less for worn guns. 28" bbls will command a higher premium as they are rare. The choke tubes might be worth more also. If it is a special edition, "1 of 1000" it's value will increase.