I listen to very quick and distorted music (grindcore) and have heard that smaller subs would be better suited for this, as long as they have enough power in them. Should I look more for decent 10's or 12's? I'm looking more for loud then quality to tell the truth, but am on a budget and would like to find a happy medium in all that.
You're right, 10's are better suited for the quick popping bass. 12's will hit the low's nicely, though. If you spend a bit of money on decent 12's, they will be able to handle mostly anything you'll throw at it. How much do you want to spend?
smaller can sound "faster", but it's not directly a matter of sub diameter, it's more the size of the box that counts.
the amount airspace in an enclosure (in relation to the sub's cone area) and the box type affects the kind of bass you'll get more so than the size of the subwoofer itself.
generally, large, sealed boxes are best for good transient response (quickness, accuracy), and the larger the box, the quicker and more accurate the bass will be.
any size sub can sound equally "fast" if it's in a large enough box. trouble is, boxes large enough to hold 12"s are usually VERY big, so 8"s or 10" are often a more practical way to get that quick, punchy sort of bass. but if you have enough room in your vehicle, you can get 12"s or even 15"s to sound very accurate and quick.
on the other hand, smaller subs don't get as loud as larger ones, so you often need to use more than one to get as loud as 12"s or 15"s. SPL vs. SQ vs. space - it's a catch 22.