Use the Nikon F. These cameras were made to be used and used hard. If you don't use it, the lubrication will dry out and you won't be able to use it.
The Nikon F2 was a more user-friendly camera than the F--and just as tough. That would be my first suggestion. I was not impressed with the F3 because many of the early models were unreliable. I hated the FM so much I never owned an FM2 or FM3. Nikkormats were good cameras and synched to 1/125, if I remember correctly.
But I would still recommend you use the F that you have.