OnlyAPerson1on a 4K monitor you will actually need to use higher DPI setting on the mouse. Otherwise it is too slow to move across the screen.
Also, and main thing, 12000 dpi will track better, more precisely, which works out nice in any shooter game - Battlefield 1, or GTA 5. etc.
Third consideration is you want a combo of mouse, keyboard and software from the same company - just to avoid overhead. Logitech has nice software with surface calibration for a mouse. They also have nice Cherry switch based keyboard for cheap 60 greenbacks. Their Romero switches are atrocious, though.