Lord D. (oh, how I like that better than typing out your full ID), if I may make one recommendation. When you begin submitting, you'll undoubtedly want to divide the magazines into three categories: (1) professional; (2) semi-pro; (3) non-paying.The difference between professional and semi-professional magazines are the amount they pay -- I think the minimum for a professional magazine is $0.03 per word (you'll want to check on that). In the realm of SF/F, only professional markets are considered at the Hugo and Nebula Awards (and though I'm not sure, I would also suspect the other major awards only look at professional markets).
I'd also suggest having between 7 and 10 magazines in each category, which would give you between 21-30 different markets. However, certain magazines will automatically be eliminated because of the kind of story you'll be submitting--for example, you're not going to submit heroic fantasy to Analog. This kind of research can be done over the course of a month or two (allowing, of course, time for sample copies to arrive and for you to read a few stories in each).
The benefit of this method is that you don't have to stop and think to whom you should send your story. The advantage is not so apparent when you're sending a story to your first market, but I found it helpful for getting to story back in the mail after receiving a rejection letter. If you have to stop and wonder who to send it to next, you may cower at the prospect of putting the story back in the mail. But when Analog says no, you know my next market is Asimov's. (Yes, I put my markets in alphabetical order.)
Once you exhaust the professional markets, you move on to the semi-professional, and then the non-paying markets. If a story goes through them all without finding a home, don't worry--as Hildy pointed out, new markets are always springing up.
One last point: Make sure you keep a submission log. You don’t want to be sending the same story to the same editor.
The best source for SF/F/H markets can be found at www.ralan.com/ .
Good luck!!
[This message has been edited by Balthasar (edited October 08, 2003).]