It must be pointed out that electron-positron collisions are much "cleaner" than proton-proton or proton-antiproton ones. That's because they are not strongly-interacting composite systems, as (anti)protons are.
When an electron and positron meet each other, they will produce a virtual photon, and with enough energy, also a virtual Z. They may also produce a virtual Higgs, but because of the electron's low mass, that particle will have a VERY small amplitude.
In fact, there's an International Linear Collider being planned, and an important question of its design is how much energy it should accelerate its electrons and positrons to. It should be enough to make interesting new particles, but it should not be enough to make the accelerator too difficult to finance.
That's where the LHC will come in. It should be able to make at least some of the particles that the ILC is to produce, and knowing their energies will help the ILC's designers work out what to shoot for.