Back when I first started playing fighting games I picked everybody and used them in a fight at least ONCE. Even if the character doesn't look appealing to you he/she might fit your play style the most, so don't steer away from a character because of their design. Steer away from them because of their move set.
After you find a character that you really like hit the training/trial modes and try to perfect some combos. Try to find out what links and what doesn't, and finally test it out against the A.I. Regardless of what anyone here says you should start with the A.I. first so you can get your reflexes ready for a real fight. You could fail if you go to training mode and hit online and get dismantled since you are not used to real fights. So, just use the A.I. to get your reflexes and AA's (Anti-airs), B&B's (Bread and butters) down so you won't have to hesitate when you're in a real fight.
Then, after you get used to your character and get a win streak going keep at it. There is bound to be a character that you don't have that much match-up experience on so until you're comfortable going against every character DO NOT switch.
After that, you should be comfortable with knowing what your play style is and be able to see what character you want to try out next. It's also important to note that when you're a beginner and trying to train multiple characters at the same time is a terrible idea. You want to stick with the same character until you know the ins-and-outs of that character.
That's how I got so good with Vega it's to the point where I was nominated and won multiple times being the best Vega on the PS3 SSF4 boards.
In short, all it takes is practice. You don't have to practice for hours and hours a day, but just set aside time for it like you would any other game and take baby steps.
I said to start with the A.I. to train your reflexes and muscle memories instead of online because some people online are REALLY good and have low points so it can be misleading. In trade you could lose interest and just be like "**** fighting games."