The best tip I could give, from my experience, is to not start a big project that you are unsure how to structure. It can lead to you getting lost in the code, and be demotivated, and possibly abandon that project. I’ve done that multiple times.
I’d suggest to start small. First make a camera that can walk around, and look around. Then give it a weapon. Etc.
In Unity, animations are usually not as mixed with the code. You can make the animations in its build-in animator, and control it through the code. If you’ve never done anything animation-wise before, I’d strongly suggest to start slow. Make a small animation. Something ridiculously small and simple. Later on, if you feel more experienced, you can make something more complex.
That being said, there is no “best way” to organise an FPS game. Every game is different, and is organised based on its individual needs. Will your game focus in weapon combat? Then maybe organise it in a way to make it easy to add new weapons. Will it focus on vehicles? Then it should be easy to add new ones. Pick a method that works, and go for it. With experience you will find it easier to organise bigger scale projects.