Visit the park's website before applying for a job. If it isn't listed in the ad, then try a search for it. The website can tell you a lot about the campground. It may answer many of your questions. Being familiar with the park's website before you make contact will also let the owner know you are taking some initiative.
Additionally, or if you can't locate the park's website, look at the website of the community where the park is located.
When you apply for a job, contact the campground using the means they specify in the ad. If there's a phone number listed, you may get the fastest results that way.
If you have connections with the community, by all means, mention them applying for a job.
If you call, be ready to tell them what you have to offer -- your skills, relevant experience, what makes qualified to do the job. However, expect that you will be asked to email or postal mail in a job application or resume. Also, if you call, keep in mind that you may reach an answering machine or someone who takes a message. Prepare a 15-second commercial advertising yourself and know your contact information; be ready to recite it to the machine as well as to anyone who answers the phone.
If you email them, send an abbreviated cover letter, just a paragraph or two. If you send a resume, send it in plain text, in the body of the email. Do not send it as an attachment unless the Help Wanted ad specifies that you should. Emails with attachments are often deleted as spam without ever being opened.
Another comment on emails.... What does your email address say about you? When you are applying for a job, it may be the first thing the employer learns about you.
I think you are better off using a functional resume than a traditional, formal one. There's really no point in listing the high school you graduated from 20 years ago. List your relevant skills, training, and experience. That means you should tell the employer the things about you that make you qualified for the job. Keep it short enough to fit on the front side of one sheet of paper. Use a plain font, such as Times New Roman, in 12-point type.
When you are preparing your resume or before you fill out the job application, figure out your references. Contact those people and ask for their permission. Gather their full names and titles, contact information, your relationship with them, etc. Don't list the references on online websites, advertising their personal email address or phone number to spammers. Do have the information handy, so that if the employer asks for it, you have it ready.
If you have two means of contacting the campground owner, I'd follow up one with the other. However, make sure your second contact adds something. If you call first, you might follow-up with an email thanking them for their time. If your first contact is by email, you might postal mail a printed copy of your resume.
If you don't receive a response within a few days to a week, do a second follow-up. Be polite. Be absolutely certain that you include correct contact information so they can reach you if they want to.
If you don't hear back after that, it probably means you are not in the running for the position. Do not expect them to notify you that they have chosen someone else.
Good luck with your job search and employment applications!