Be aware that most (but not all) F connectors are for 75 ohm coax, the coax cables you mentioned are 50 ohm. N types are also mostly 50 ohm, and I've only ever seen 50 ohm TNCs although I believe 75 ohm ones exist.
Also be aware that sticking a 50 ohm N plug into a 75 ohm N receptacle won't end well!
You can get N to F interseries adapters, I have one in my selection.
All the GPS terminations I've ever seen are 50 ohm.
Assuming the antenna's active, it'll have plenty of gain and you will probably find you can get away with quite a bit including an unmatched 75 to 50 ohm transition.