http://www.sirlin.net/ptw/ (Very good read to get you into a more realistic fighting game mentality)
http://www.sirlin.net/archive/my-street-fighter-tutorial-videos-from-ccc2/ (Tutorial video for Super Street Fighter 2 Turbo also known as ST for short)
http://sonichurricane.com/articles/sfterms.html (A list of fighting game terms widely used)
Buy a stick, practice at home. Getting an expensive stick is not really important right now, you just want one that can hold you over for a while, so you can really get the hang of things.
The most important thing to not do when your starting out is to NOT go into practice mode without a reason. You want to get straight to the point in practice mode to not waste time doing anything else. If your going to practice a certain combo, make you hit 100% of the time. A good way to do this is:
Hit it ten times in a row from the left. If not, start over.
Hit it ten times in a row from the right. If not start over.
Go into the arcade mode and do it at least five times.
Find a sparing partner to help you, someone with as much drive as you, or a mentor. Without this, it is considerably harder to become better. It is very important for your questions to get answered not only online, but with someone else. It also helps when there is a team tourney, so you can already have a partner. Also, the most detrimental thing that stops people from becoming better or playing more is location. If your in a area with a strong scene, take full advantage. Fighting other players is going to be the only thing you can do to get better once you reach a certain point.
That thread has a list of interviews from several extremely good Street Fighter 3: 3rd Strike players. Even if 3rd Strike (3S) isn’t the game you want to get good at, its pretty much the main game of the fighting game community right now, and it wouldn’t hurt to try an learn it. I mostly play Guilty Gear, and these Podcasts are extremely helpful to me., and I’m currently playing 3S now because of these podcasts.
And as for a game that can help you get better in fighting games in general, it is definitely ST. If you can, try to get it for GGPO or 2DF, and you’ll start getting the basic jist of things. SF4 plays extremely similar to it, and if you have very strong ST fundamentals, you don’t need to know all the Focus/Saving Attack mechanics.