Evil Ed gave you some good advice. I'm going to chime in too.
First, ask yourself what are your goals? What do you want out of handgun shooting? Fun, just to plink? Or are you looking for a home defense weapon? Do you want to shoot competition? Once you answered those questions, you can go from there.
My personal area of "expertise" is in tactical/defensive shooting. So I shall speak to that end. Get some good quality training under your belt. I've said this before: You can't go wrong going to one of the big schools out there. Gunsite, Blackwater Lodge, ThunderRanch, etc. Having said that, I URGE you to check your ego and not try to enroll in an intermediate or advanced class. Start with a good basic course and go from there. With as much training as I have, I never go to someone's advanced course. I always start off low and work up at a new school. Everyone has their own subtle changes to the basics. I hate being behind the power curve.
After that, practice. LOTS and LOTS of practice. Doesn't have to be live fire. In fact, I generally use a ratio of 70% dry fire to 30% live fire. A high speed shooter is merely someone who has mastered the basics and can perform them in a compressed time frame, under stress/duress.
Continue to train with competent, solid instructors, whenever you can. I strongly urge you to conduct background checks on your instructors. By that I mean, check into their qualifications. Were they really a Navy Seal? Where they really a "black op" CIA agent? Did they really win the gunfight at the OK Corral? If they are a former police officer, find out why? There could be a myrid of reasons; however, some of them are bad reasons.
Ask for a copy of DD214's (military discharge papers). Ask for a copy of the police reports for all the "bad guys" they have killed. If they can't provide said information, I would take a good hard second look (think BS). No use having been taught by some yahoo and ending up in court. Said yahoo aint going to be there to back you. Do your homework. You'll look alot better for it.
Finally, you can keep somewhat up to date with internet boards, such as this. Books, videos, etc are good. However, NOTHING beats real training from a solid, well rounded instructor.
Oh, by the way, did I mention PRACTICE???