I focus on two or three companies that meet my threshold for a good opportunity to learn. Get the company directory - it is not easy to find but it is out there - find the individuals who have hiring authority and direct your energies directly to them, not HR. Letters to the individuals should be 1 page only and brief as possible. You have one chance to make a first impression so spell check. Good luck.
Helpful article on creating and working a job search plan:
http://www.expert-career-advice.com/job-search-plan.html