Since the avowed purpose of the Death Penalty (as stated by those who support it) is that it serves as a deterrent, your thesis supporting it should reflect this fact. Your research should cover particularly heinous crimes for which the penalty was imposed, such as the Oklahoma City bombing, child murders, etc. To the extent you can do so, your thesis should negate the argument that it is based on revenge rather than deterrence. You should also be prepared to argue that its deterrent value far outweighs the cost of its imposition. Finally, be careful to avoid hyperbole; keep your argument matter of fact and free from emotional appeal. This may be hard to do, as there are few issues more emotional than that of capital punishment; still frame your argument in terms of compelling reason as opposed to impassioned pleading. Good luck!