You don't necessarily need an mfa. If it makes sense for you to earn the degree, by all means, go for it; if not, don't sweat the fact you don't have one, and certainly don't apologize for it in your query letter. While the degree is generally more pertinent to literary fiction folks than to most other authors, no one will fault you for not pursuing it. As I've mentioned before, you don't (thankfully!) need any kind of professional licensure to write.
You don't necessarily need any prior publications. By all means, if you've published short stories in literary magazines like Harper's, The New Yorker, or The Paris Review, I think you should mention it in your query, but again, don't apologize for what you don't have. If you don't have any short story credits, don't bring up the subject. Again, these are more helpful to the aspiring literary fiction writer than to most others (except, I think, poets), but don't think that you have no business querying agents with your novel simply because you don't have a sterling short story publishing track record.
Short story collections don't sell very well. You're much better off pitching a novel than a collection of short stories, although if you're a total literary badass you might be able to get an agent to take your collection on the condition that they also get your début novel. I wouldn't count on this, though, so if you've got a bunch of polished short stories lying around, you might want to send those out to literary journals and magazines while you prepare your novel for submission to agents.
It's all about the writing, but you still need a plot. Beautiful writing will attract an agent's attention, but without a coherent plot, your novel is little more than a series of character studies. Things have to happen. People have to want things. People have to lose things. You might not have vampires fleeing werewolves or master detectives tracking jewel thieves or starship captains trying to get home from the far side of the galaxy, but you need something that drives your characters forward, a series of events that will deeply engage your reader, something that your book can be about. I've seen a lot of manuscripts with great writing but in which, unfortunately, nothing happens. Don't fall into this trap.
That's all for now, gentle readers, but I encourage you to ask any questions or post any additional tips in the comments. I'll be at bea for the next couple of days, so I might not be responding to comments very regularly, but I'll do my best to answer any questions that crop up.