How are particles in a collision chosen? In synchrotron particle colliders, how are the particles which are collided chosen?  For the most part, collisions of different types of particles don't do anything like you might expect in a video game; there is no secret recipe list of cool things, each which require different types of particles.  So, what makes certain particles more favorable than others?  
 A: It comes down to a trade-off between collision energy and collision 'purity'. Accelerating lighter particles, like electrons, to high energies is difficult because they have higher synchrotron losses. It is easier to accelerate protons to higher energies, however their collisions are 'messier' - the interactions that happen during collisions are much more complex and harder to predict, and so you actually need a higher amount of energy to see the same kinds of particles.
For certain kinds of experiments, and certain kinds of accelerator designs, it's actually preferable to collide elementary particles instead of protons. And for other kinds of experiments, it's preferable to collide much heavier particles, such as lead nuclei.
A: In rough lines, when one is planning a particle collider experiment, one has a theory which will be tested by the experiments in the collider.  
There are two streams :discovery machines, as was the Tevatron and now the LHC, which by discovering new predicted by the theory particles validate the theories, and accuracy machines , as was LEP, the electron positron collider, and the future ILC. 
Hadronic collisions have much higher cross sections and as the other answer explains can go, due to their mass, to much higher energies, opening channels not available to the lower energy (per force) electron positron colliders.But the theory is very messy because of QCD and no accurate theory predictions can be checked or fitted. The electron positron collisions have much simpler feynman diagram contributions in the calculations, and thus a theory can be fitted with small errors, as was the standard model fitted at LEP.
I think it was Feynman( or maybe somebody else, I like it as an analogy) who said :"if you want to study the inside of a clock you do not bang two clocks against each other and count the fallen gears, you use a screw driver " .
So it depends on what the people proposing the machines want to do. Go for accuracy, or for spectacular new particles, which will herald supersymetry, the proposed extension of the standard model.
