It is very difficult answer which are the best DPI settings for an FPS. There any too many different variables like the mouse device self (resolution, weight, etc.), the material/brand of your mouse pad or the surface if you haven't one, your hand posture and the force you apply, etc.
Then it depends also how the game implements the mouse input, and even sometimes depends on the class you are using. For example in Team Fortress 2 I use two different settings if I play Sniper or I use Heavy instead.
In the end, if it can help, I suggest you to define as many different profiles as your mouse control software can support (3, 5 or more) and set constant DPI interval between them.
For example I set my Logitech profiles to 800-1000-1200-1400-1600 DPI and then in-game I can easily change between them using the dedicated buttons.