How many resumes/cover letters do you think I'll need in order to actually get an interview and a job?
Depends on what you put in the letter/resume. In my experience, you will either get a response quickly or no response at all, so your best strategy is to find recent job postings and apply to them quickly. In other words, every morning and evening search for new job postings and apply to them. Repeat until you get a job offer.