My first story is on its third publisher. One rejection was very personalized and positive with reader commentary. Another was personalized enough to include my name and my story's title. This one sent an email acknowledgment with a personal response to my cover letter. Not every place gives you a critique (thank you to the editors that do!), but definitely note what they say.
What can I recommend? Research the markets to exhaustion. Writer’s Market used to be the end all, be all, of how to find a publisher or an agent. Perhaps, for novels, they still are. Query Tracker is another great source for agents and publishers. Cheat mode: do enough google searches and you’ll find every magazine of every genre and every age, plus most have websites with submission guidelines. If you learn which editors want what, you’re more likely to get acceptance, or at the least, pleasant rejections.
Did you proofread? Run the spell checker. Now read your story for errors it won’t catch. Did you know there is one space between a period and the start of a new sentence? Thanks, Mrs Something from grade school, but they changed the rules.
Learn to format. Learn to read every detail of the publishers preferred format. Go look at Proper Manuscript Format. Some will tell you this is all they will look at, and others will throw this out the window. I learned it the hard way, then got a program that does it automatically for me. I always check over the compiled result and make sure it fits the criteria.
There are a variety of rejection letters, this article being the one I found the most helpful. Did you know you can actually reply to a rejection letter? The article by Nathaniel Tower gives some advice on how to respond to each type.