It is a tad old a this point, but the FPS tutorial I wrote for the Godot documentation shows how to make a simple FPS game in Godot, complete with animations.
Though the tutorial does not cover making the 3D models or animations themselves. As @cybereality said, you will need to use a program like Blender for the 3D modeling, rigging/skinning, and animating of the guns. Godot’s AnimationPlayer node may work as an alternative for animating in Blender, depending on how the 3D models are setup and the desired results.
(Side note: Welcome to the forums!)