The new hadron collider at Geneva (Cern) is on the verge of bringing bits of matter together at speeds of about 99.999% that of light. When some of them do slam together, the heat generated is supposedly in the billions of degrees K. My question is: are we looking to find what matter was prior to the BB, or is it the instant following, when everything was a plasma?

LHC is not built to bring evidence about conditions before the big bang. It is in fact not constructed to explore the big bang, either (consider that rumor a very successful marketing gag). LHC findings might help understanding the conditions after the Big Bang better, though. For example, it is better to predict which particles were created in which stage after the Big Bang at which rate if you know which particles actually do exist . The main goal is understanding particle physics at energy scales around 100 GeV to maybe 1 TeV better and find new particles (in the proton mode) - irrespective of a possible "real-world" applications.