If you have access to an arcade stick (or are willing to buy one), I'd start with Super Street Fighter 2 Turbo. It's cheap, easy to pick up and play (assuming you're already familiar with Fireball and Dragon Punch motions), and introduces a lot of the archetypes that are in pretty much every fighting game, so you'll have a baseline level of skill at practically any other fighter. The guys over at Shoryuken also put together an Ebook about getting into Fighting Games, focusing on Street Fighter 2 that I think is pretty solid at conveying what you need to know to get the hang of it.
If you don't want to make that kind of monetary commitment to the genre just yet, I'd recommend giving P4A or a Marvel game a shot, because they use a 4-button control sceme rather than a 6-button setup, which makes them easy to learn on a gamepad. They're pretty simple, control-wise, and offer up a lot of the basics. My only complaint with Marvel is that it kind of goes bananas pretty quickly, so it's tough to get the hang of the basics if you're a beginner.
Also, the new Killer instinct's training mode is one of the best I've ever seen at introducing fighting game concepts. It'll teach you about spacing, combos, and even go into how the systems of a fighting game work. It's a great primer for the genre, and it's really easy to pick up and play.