I have "broken into" selling to magazines, but with much different subject matter (wildlife). I will tell you what I have learned about the business after several years of both failures and successes:
Most publishers will not accept images from any other than a few select photographers that they already have a well-established working relationship with. Magazine staff members are busy people with a lot of work to do. Like everyone else with a job to do, they want to get it done as quickly and efficiently as possible - this is most easily accomplished when they work with contributors that they already know, and have "in the system". Remember that many of these people don't take much time deciding what photos to use in the magazine - as long as they have something decent to fill the page, they've done their job and can move on to the next task.
My advice is to be honest with yourself about your imagery. Look thru the pages of the magazines you want to submit to, and realize that your work will have to be both better than what is there, and different from what is there.
Also realize that, when you see an image that is in there that doesn't seem to be as good as some of yours, that it may very well have been taken by the author of the article it is supporting, or it could be one that was taken by a member of the editorial staff. Magazines will always prefer to use images that are submitted as part of a "text/photos package", and to use images taken by their own staff members. It is both cheaper and easier to do so, and they don't really care that the photos may not be as good as ones from other sources.
When making initial contact with the editor or art director, do not ask if you can submit images to them - rather, ask if they would send you their submission guidelines. That is a more professional approach, and shows that you are familiar with the publishing industry and how it works.
Do not be surprised if the submission guidelines state that they will only accept unedited, unmanipulated images. Many magazines have an art director with a graphics design background, and he will prefer unedited files to work with so that he can do the editing himself (if any editing is even required). For this reason, it is very important to get the images as good as possible in the camera, because the SOOC images are what they will be seeing when they review your submission. Most of the magazines I submit to require unedited image files, and, oddly enough, they frequently don't even bother to edit them before printing. I submit an unedited version of the photo, and they often take it just as it is and print it that way. So, getting it right in the camera really is very important.
"Your" and "you're" are different words with completely different meanings - please use the correct one.
"They're", "their", and "there" are different words with completely different meanings - please use the correct one.
"Fare" and "fair" are different words with completely different meanings - please use the correct one. The proper expression is "moot point", NOT "mute point".