I've got a list of about 100 lit mags that are very difficult to tell apart in terms of content (though they would scream bloody murder to be characterized that way). A lot of them are supported by universities and have a frequently changing editorial staff. For all of them, it boils down to understanding the personal tastes and stylistic preferences of one or two people (a first reader and a fiction editor). This can be done to some extent by reading recent issues and the website, and by googling the names of the editors (since they do sometimes get interviewed by blogs). But I do believe that every submission is a bit of a crap shoot in this market.
I volunteered at this
lit mag as a first reader (screams bloody murder), and from that experience alone, I'd contradict some of the things people have said here. For one thing, I'm pretty sure no-one there cared about the genre of submissions. In fact, I'm halfway through writing a spec-fic piece for them now.
The thing was, although we received the occasional piece of (for eg) sci-fi, it was generally awful. That's not really surprising - of the 100 or so pieces I looked at while I was there, I could only put forward two for publication (and then reservedly). So given that about 4 or 5 were sci-fi, that doesn't give much info about your odds.
The main thing to keep in mind with literary mags is probably the different focus on what they look for in a story - Isaac Asimov (whose short fiction I adore) might never have gotten so much as a mention, because his writing style is relatively bland. Ideas aren't completely discarded, but the only piece I'm aware of having gotten in on the strength of my recommendation revolved around a rape, which I'll be the first to admit is a trite subject in the short fiction genre.
So in other words, a lit mag might accept a sci-fi story that a sci-fi mag would snub and vice versa. The editor of the mag I worked at was seriously contemplating a sci-fi themed issue at one stage, but he decided against it primarily (I think) because of the difficulty of finding people who know enough science to write even vaguely convincing SF who can write their own name without resorting to cliche.
Also (and this is just my own preference, which I can't generalise), in such an environment I didn't give a monkey's whether the writer had read, or could prove she had read the magazine. My favourite cover letter ever was (I hope coincidentally) the one from the rape piece. It's entire content was something like 'I'm a student at [bla]. In my spare time I like to write.'
So (still my own preference), the worst thing you could do in a cover letter was make it extensive - before you persuade me otherwise, I'm going into your story with an open mind. All the letter does is give me a chance to dislike you first. And call me impatient, but I know where I'm working, so I don't need you to restate the mag's ethos. I'm also evaluating the story you've sent me, so I don't need cajoling with a long list of your professional writing degrees, publications in other mags or comments that friends have made.
One thing about smaller mags in general: since you're competing against fewer authors, not only is your story statistically more likely to get published, but you're also more likely to receive feedback on it.
Oh, and more important than targeting your subject matter (IMO) is targeting your prestige. The mag I worked at specifically (albeit not exclusively) seeks out writing from new authors, although looking at their 'about us' page, they're somewhat cryptic about it. Still, if a mag is boasting exclusively about big names who're writing for them
at the moment, that's probably a good reason not to waste your time submitting.
And lastly, don't be afraid to look abroad. No-one cares where you're from, as long as you can use the lingo.
