PC version: Moving with your mouse- help please?

I originally bought hitman 2 on PS2 and completed it and enjoyed it quite a lot so I just bought contracts (PC version). I'm on the first mission and i've found the controls to be relatively easy to get to grips with on the keyboard, but when I try to move the mouse it doesn't seem to respond very quick to my movements. I tried just charging in and killing the enemies which is the tactic that usually works but I keep getting shot because my mouse is slow at reacting when I try and turn directions up, down or to the side to shoot the enemy. My mouse is brand new too and its a gamer mouse, i rarely play PC games but I was just wondering if anyone else has had this problem, if so:

How can i fix it so that my mouse responds quicker???


Also whenever a menu screen is there I have my normal mouse curser and the built in curser on the game and they're both on the screen at the same time, how do I get rid of one of them so that theres only one cursor on the screen at any one time???

thanks