You don't need a "gaming" mouse. Any halfway decent mouse works better than a controller. Most "gaming" peripherals are overpriced for what they are.
Steam will tell you if a game supports the xbox 360 controller in this area on the store page.
From MW3:
No reason to buy blindly in the future. If the "Controller Enabled" icon isn't there, it won't be natively supported.
Here is an example of a game that supports the 360 controller (Bastion in this case):
Thanks. This will come in handy.