The XInput standard of 8,000 will typically be used in profiles for analog sticks. For an Xbox 360 controller, that value tends to be the best minimum value to ensure that no unintentional events are produced due to what position a stick will be centered at.
When using a different controller, you will likely want to play with the value of the dead zone used for the analog sticks and find what works best for your controller. As an example, when I make profiles for my Logitech F310 gamepad, I find that using a dead zone value of 2,000 for the analog sticks works best.
The default diagonal range of 45 degrees is recommended when mapping keyboard keys to an analog stick when using the standard stick mode. If only one action should ever occur at a time and the diagonal direction doesn't matter as much, you might want to look into 4-way cardinal stick mode. That can be useful for navigating menus or mapping weapon hotkeys to an analog stick.
Some games will overreact when mapping WASD or other keyboard keys to an analog stick. This is mainly due to how quickly directions can be changed especially if you have the stick positioned right around where a diagonal zone resides. If you encounter problems in game or you just want to make movement a little more definitive, you can adjust the stick delay value used for that stick. That will cause direction changes to be slightly delayed. Even setting the value to 0.01 seconds can greatly increase control in some games.
To allow for better mouse control with an analog stick, it is recommended that you use a diagonal range of at least 65 degrees instead of the normal 45 degree value. If you want more twitchy mouse control, you will likely want to set the diagonal range of the stick to 89 degrees or 90 degrees. This will minimize the range used for the absolute cardinal directions.
Another tip that will allow for more twitchy mouse control is related to the dead zone used for the analog stick. Decreasing the value used for the stick dead zone can help make mouse control feel more responsive than when using the standard value of 8,000 even when using an Xbox 360 controller.
Based on my experience, even decreasing the value to 6,000 can make a huge difference. The big compromise is that there might be some mouse cursor drift if the analog stick does not center back to the assigned dead zone. On my Xbox 360 controller, I find that the stick can get stuck slightly in the southwest region of the stick; the other directions don't have this issue. However, the mouse cursor drift is very minimal and you can easily compensate while playing a game. It doesn't hinder gameplay and the benefit obtained far outweights the minor problem.
One final thing that you can do to make mouse movement more twitchy is to enable extra acceleration for mouse events. Changing the extra duration of acceleration will have the biggest impact on mouse movement. Increasing the maximum extra duration of the acceleration will loosen the mouse movement. Changing the multiplier is another option that will change how mouse movement behaves. One final option that can be changed is to use a different curve for extra acceleration. Linear is still the default setting since it was the only option available for many versions but I find myself using Ease Out Quad lately. Besides altering the final multiplier used, it also changes the final duration experienced.
With all the options available for extra acceleration, you will have an easier time performing a quick 180 degree turn while still having precision on the low end of a stick for aiming at targets.
It is generally recommended that you specify action names when making profiles that you will share with other people. This will allow other people to more easily decipher what buttons are used for in a profile. Specifying action names can also be a helpful reminder for yourself in order to document a more complex action.