The parametric EQ is the most flexible type of EQ. It operates just like a sweepable EQ but gives you one other control, the bandwidth, or Q. With the bandwidth control you can choose whether you're cutting or boosting a large range of frequencies or a very specific range of frequencies. For example, you might boost a four-octave band centered at 1000Hz, or you might cut a very narrow band of frequencies, a quarter of an octave wide, centered at 1000Hz.
A graphic EQ is way different, not quite as flexible. You can actually see graphically which frequencies are cut and boosted by looking at the sliders. Each slider is called a band and it represents a frequency. The bandwidth on a 10-band graphic is one octave. The bandwidth on a 31-band graphic is one third of an octave. Obviously the more bands you have the more precise you can get in shaping your sound.
I don't think any particular brand lends itself to any style of music it's basically how you use it to shape your sound. As far as brands go check out Rane, ART, DBX, Presonus.
Hope this helps!