I think I just noticed that I've done a very bad mistake when picking until now but I just want to know what you think. Before when I picked, I did not care if the picking hand was close to or touching the bridge. Instead my picking had was picking the strings really close to the neck. Because of this the pick did not have enough angle to the string and the strings are easier to bend closer to the neck than the bridge. So my pick kept getting stuck in the strings when picking and I had problems picking fast. Now when I tried keeping the picking hand so that it always touches or is closer to the bridge, I think the picking became much easier. Is this "the right way" of doing it, do keep the picking hand close to the bridge so that you are touching it to get the right angle and to hit the strings where they do not bend as easy?
You actually will want to practice picking at different areas depending on what you are playing. For heavy tones this is less useful, but for clean or dirty clean tones where you pick can have a great effect on the tone.
The only time I pick close to the bridge is if I want a really brittle, thin tone. It sounds metallic, good for some things like shoegaze. But playing leads or rhythms there sounds shoddy to me.

The generally best area of picking is the middle area between the end of the neck and the beginning of your bridge. Depending on your pickup selection, you might want to migrate your picking point towards that pickup.

Also, how does your pick get "stuck" in the strings?
Its probably easier to pick close to the bridge because of higher string tension but the closer you get the weaker the attack will be, I like to pick approximately where the neck humbucker starts.
I like picking near the neck for deeper tones or when I'm playing cleans, but if I'm palm muting or doing distortion I'll pick near the bridge or the middle. The middle is the best IMO, but you can get some cool dynamics if you change where you pick certain notes during a riff or lick.
Different spots are good for different sounds. I find the closer to the neck you are, the more mellow it sounds (to me, anyway). There's actually quite a bit your right hand can be doing when it comes to picking. Even angling the pick can change the timbre of your lines slightly.

Lately I've been experimenting with laying my palm on the bridge (floating trem) and shaking the trem block to effect. It's kinda cool
I keep my picking hand right over my bridge most of the time so I can hit palm mutes whenever I need them. Like others have said, different areas on the string will produce different tones. If you find you are playing better with this new position I think it's a good idea to stick with it
For rock, close to the bridge makes sense. Less string movement and more biting sound. Plus you have the option of muting which is common in rock.