Choosing appropriate screens for an extrusion process involves striking a balance between filtration needs (removing more contaminants) and overheating. Finer screens get more contaminants out, but they also raise back-pressure in the extruder, which requires more power from the motor and, thus, creates more frictional heat. Barrel cooling may help, but it isn't efficient because it raises viscosity on the barrel wall and makes the motor work even harder, putting back some of the heat taken out by the coolant. Finer screens also need to be changed more frequently.

Screens are often put in as a screen pack, with two, three or more screens of different meshes. Most packs have the coarsest screen up against the breaker plate to support the others, but putting it in "backward" also works, as the bigger particles get caught first and never reach the finest screen. The packs may be premade and put in baggies until needed, spot-welded together to ensure they stay in the right order or may have a crimped aluminum edge, which holds the screens together while serving as a gasket to prevent leakage.

Some useful tips:

To get finer screening without finer screens, cross any two similar screens at a 45 degree angle to each other.
Pay attention to wire gauge. Thin wire means bigger holes and less filtration, and the screen will be more likely to tear under high pressure differential.
To ensure the screens are put in the same way every time, use symmetric packs; that may waste a few screens but it avoids errors.
When specifying/buying screens in areas where metric and American systems are both used, make sure you know whether the numbers are wires per inch or per centimeter.
With corrosive resins such as PVDC, CPVC and some fluoroplastics, special metals are necessary. For PVC, steel is OK, but many PVC lines do without screens to avoid the overheating noted above, which may require a more expensive formulation.
Consider Dutch weave or Dutch twill, if you want a single thick/rigid screen and fine filtration.
For very fine filtration, consider sintered metal-fiber disks or extended-area "candles," as used in textile spinning.
For highly contaminated feed, consider a self-purging changer.
Make sure your pressure gauge is working right, as it will tell you when it's time to change screens.