There is no Remington Model 6 pistol, there has been however cases however of Remington Model 6 rifles converted to pistols by gun or "home" smiths. NOT Remington. As such the value is whatever someone will pay, but generally not much.
100-1000 USD or more depending on specifics
Seen this model on Gun Broker.com, asking price was between $575 and $650.
These where manufactured from 1981-1987. If in 90% condition then about $300.
According to Remington's website, that model was made 1928-1933.
Just like a car is it in the showroom or the junkyard, value is determined by condition, condition, condition, and condition.
your Remington model 6 was made in 1998,due to the S prefix on the serial#.
6 t0 7 hundred dollars
I don't believe there ia a model 19, a semi-auto? Possibly a 16? Is it a semi-auto 6 shot?
It is unusual vs. rare
You first have to identify which model and then you need a good description of it's condition. A guess would be a model 4. Try the Remington firearms model history page and look at the model 4 or the later model 6 they have photo's they don't however have anything on the earlier models.
http://remingtonsociety.com/rsa/service