I have a Dremel these days, it's bloody terrific, and good for a plethora of non-hobby uses. My original power tool was a no-names cheap thing, which didn't have variable speed and its accessories were not good (snapped drill bits in the eye sucks a LOT, particularly when you have to drive yourself to hospital at night), eventually I tossed it. Dremels are expensive compared to other brands, however I tend to go with the "get what you pay for" theory. They have a squillion accessories, and very good drill bits, polishers, grinders, cut-off wheels and so on.
If you're going to be doing extremely fine cutting work, use the jeweller's saw, as sawgunner101 says, even on low speeds you'll find they go too quick.
Summary:
wired power supply
variable speed
WEAR GOGGLES!!! I have a permanent "black spot" in my left eye due to not following this piece of advice....it is NOT cool.
cheers
duckman