For Unreal Tournament 99 (UT99), you should use a mouse with a low DPI (400-800) and a standard polling rate of 1000 Hz. It is crucial to disable mouse acceleration in both the game's settings (enable "DirectInput" and disable "Mouse Smoothing") and in Windows ("Enhanced Pointer Precision") to ensure consistent, predictable aiming. You may also want to install an updated renderer, such as the d3d9 renderer, and set a frame rate limit in the game's configuration file to match your monitor's refresh rate for smoother gameplay, as suggested in Steam Community.

Mouse settings
Mouse DPI: Use a low setting, such as 400 or 800 DPI, for the best results.
Polling Rate: Use a standard 1000 Hz polling rate. Higher rates can cause issues with the old game engine.

In-game settings
Enable DirectInput: Go to the "Input" tab in the game's preferences and make sure "DirectInput" is ticked.
Disable Mouse Smoothing: Also in the "Input" tab, turn off "Mouse Smoothing".
Set Frame Rate Limit: Install an updated renderer (like the d3d9 renderer) and set the Frameratelimit value in the unrealtournament.ini file to match your monitor's refresh rate. You can find this in the [D3D9Drv.D3D9RenderDevice] section of the .ini file.
Disable VSync: Turn off VSync, or disable it by setting the SwapInterval to 0 in the .ini file.
Windows settings
Disable Enhanced Pointer Precision: Go to your Windows mouse settings and turn off "Enhance pointer precision" to disable mouse acceleration.

Tips
Test and adjust: These are general guidelines, so be sure to test what feels best for your setup.
Adjust sensitivity: You will need to find a good in-game sensitivity that allows for both quick turns and precise aiming. A good rule of thumb is to set it low enough to be able to hit a distant target with a sniper rifle, but high enough to do a 180-degree turn with a single mouse swipe