99F.
1899F was saddle ring carbine. Earlier model.
And therein lies part of the confusion. The 1899F was never catalogued as the 1899F - it was simply the model 1899 carbine. The nomenclature 1899F was created in the 80's (by Doug Murray as far as I know) to lend some clarity to catalogued 1899's. The "F" was from the cable code used to order that model.
I don't believe Savage by itself ever really had a moment of "We're now going to call our rifles 99's rather than 1899's". They did have a moment in 1921 where they finally decided to come up with models for the rifles and called them 99's rather than 1899's. But they continued to refer to them as 1899's in some ads after that for the simple reason that everybody back then knew what they were talking about. If they referred to a model 1899F in 1925 everybody knew they meant the 99F - because there had never been a model 1899F. I would presume the Winchester 1894 to 94 name change was similar.
This is also what confuses so many people who think there must be physical differences between the late 1899's and early 99's - but there aren't. It was simply a catalog name change.