As of version 4.30, default input profiles for the Saitek X52 and the Thrustmaster HOTAS Warthog are now available in addition to the generic default profile for joysticks.
Backing up your Input Profile
For those of you who already have existing input profiles and do not want to risk losing these profiles when trying out defaults, I would suggest backing up your existing profile. You can do this by scrolling to the very bottom of the Controls submenu of the Options menu and activating "Save Profile" to save your existing profile. You can later load that profile to restore to an input state that you are reasonably satisfied with.
Activating your Devices
Before loading the default profiles for joysticks, use "Manage Controllers/Joysticks" to make sure that your input devices are active. If using an input method comprised of multiple devices such as some stick+throttle combos, make sure that the stick is at the first position, while the throttle is at the second position. If using a stand-alone stick, make sure that your stick is at the first position.
Bi-directional Throttle
If you prefer, or have to, use a throttle device's entire range of motion to only control forward movement, such as when using a throttle with no center notch, you could deactivate the setting "Bi-directional Throttle". Note, however, that this can cause problems with other input devices such as gamepads or the Oculus Touch controller that expect this setting to be active.
Automatic Target Selection
With automatic target selection on, targets that are directly in front of your ship are automatically selected. In 3D mode, this automatically selects what you look at. The default joystick profiles were designed with this setting active, but with buttons also mapped to select targets, this can be safely turned off.
If automatic target selection is on, it is useful to have a control mapped to "Toggle Target Lock".