About the F style...

What is an F style mandolin
The 'F' stands for florentine, a reference to the scroll that forms part of the instrument body
What is the History behind the shape
It seems to start with a Mr Orville Gibson in the 1890s. He built only a few instruments including Mandolins,Guitars and hybrid guitar/mandolin/harp specials. He had two basic Mandolin shapes the symetrical 'A' and fancy 'F'.
The Gibson company (early 1900s) used his basic shapes and name for all their mandolins/ Mandolin family, although they have not made mandolins with oval soundholes for years.
Who where they made for
The Gibson mandolins were targeted at the Mandolin orchestra which was popular at that time
Why the association with Bluegrass
The Gibson mandolins built for the mandolin Orchestras of the early 1900s sounded better in a Bluegrass band than the bowl backed mandolins.
The F5 (first built in the early 1920s) was the only Gibson that had 'F' holes, it is the preferred mandolin shape for most Bluegrass players.
Whats available today
Vintage Gibsons have that aged sound, the only affordable ones have oval soundholes. An early 'F' hole Gibson can cost 20-30,000 dollars or more. Gibsons made after the 30's have a bad name. Modern gibsons have a better name but they are massed produced. For similar price of a Modern Gibson you can have one hand built by one of the many builders around the world. I have seen and heard excellent F5 copies from America, England, Czech Rep and Australia.
More Information
See our links section to areas such as Mandolin Cafe' etc.