If I have shielded cables, jacks and plugs and I ground the shielding properly, then should I use shielded plugs at the computer's site too? I mean if I do so, then the shielding will be connected to the motherboard or to the case, which I am not sure I want...
Shields are tricky, as the likelihood of introducing a ground loop when using them is rather high. This could lead to unpredictable performance issues.
Shields are optional on Ethernet, and the connection itself is galvanically isolated from the PC. The interface can tolerate more than 1kV difference between both sides and the cable common-mode is terminated, thus reducing EMI generated/accepted interference.
Common practice is to ground the shield only on one side of the connection, thus providing a path to ground while avoiding the potential ground loop.
Shielding either protects the inner conductor from external fields or prevents the cable from radiating radio emissions. Another use for shielding is to shield the cables from static shock from a user or being dragged on the floor (which generates considerable charge). Most digital signals don't need shielding because they have ways of minimizing noise. For example, Ethernet, USB, SATA and many other buses use differential signaling to minimize noise. And most employ CRC or some kind of error correction/detection to reduce noise further.
For the cables that do has shields such as USB, the shield is tied to the motherboards ground or chassis ground. The shield only needs to be tied to a ground, and the closer to the cable input the better to minimize inductance that may prevent the shield from being effective at high frequencies. Cables that could experience large static shocks (from humans) should have the shield tied to chassis ground to route the current away from the products ground plane.
There isn't a 'best way' with electromagnetic compatibility engineering because it really depends on the application.