A cover letter and resume are two pages together, no more, no less (except for cases of extreme specialization).
Page One: Cover Letter
A cover letter should be three paragraphs. 1.) Greeting and why you're bothering them. 2.) Your current job role, how your knowledge and skill will benefit the company and why it would benefit you and the prospective employer to hire you. 3.) You want to speak with them over the phone or in person about the job, basically you are scheduling an interview proactively. Thank you, and done.
Remember this is a business letter! Do not indent. Do not use warm fuzzy greetings, strange fonts, etc. Date goes at the top, followed by your (sender) details followed by their (recipient) details followed by the body. Don't change this!
Page Two: Resume
Section #1: Name, telephone number, email address, current FULL address, current job title (what are you, anyway? Engineer, Accountant, etc).
Section #2: Statement of intent and/or objective. This is what you want to do and why you want to do it.
Section #3: Relevant work experience from the last 10 years to backup the previous section. If you don't have it, list the jobs with the most responsibility or tenure.
Section #4: Education and Certification: Where you went and what you got. Keep this simple.
That's it folks. Don't need anything else. Don't need to know you like puppies or that you were part of the chess club or anything else. This formula has worked well for me, it will work well for you. Remember the resume is just one page. You will need to be specific but brief and your formatting must be clean and readable. No text walls!
I haven't seen a paper resume in ten years. Most recently, in the last five years or so, I have used PDFs. They look far more professional than a Word document.