There is no universal best DPI
Mouse DPI is one part of a larger control system. Your game sensitivity, mousepad size, grip, resolution, operating-system settings and personal control all affect the result. A setting that works for one player may feel uncomfortable for another.
A practical starting range
Many desktop and gaming setups use values such as 400, 800, 1200 or 1600 DPI, but these are starting points rather than rules. Choose a value that gives you enough physical range without making normal cursor movement inconvenient.
Low versus high DPI
Lower DPI paired with an appropriate game sensitivity can require more physical mouse movement for a given turn. Higher DPI can allow smaller physical movements, but the game sensitivity should be adjusted if you want a comparable overall sensitivity.
For FPS games
Competitive FPS players often prioritize consistent, controllable physical movement. Instead of chasing a particular DPI number, document DPI, in-game sensitivity and cm/360. A large mousepad gives more room for lower-sensitivity setups, while smaller desks may encourage a different balance.
Test your setup
Start with one configuration, run your preferred game drills, and change only one variable at a time. The DPI Analyzer, eDPI Calculator and cm/360 Calculator can help document the numbers.