As far as what size styrene to get, it depends, on the kit, and the scale.
Personally, I would get a couple of "odds and ends"packs. I think that those will get you started, all kinds of different junk in those.
As far as cutting: Dremels are great for quick sloppy destruction, but terrible for presicion cutting.
(Through PLASTIC, anyway!! They rotate too quickly, and they end up burning/melting, as much as they grind/cut.)
For cutting plastic, you need a good razor saw, xacto, or?
Most of the time, I use the back of an exacto knife, but I do have a razor saw, and a blade, it depends on how precise,of a cut, as to what tool to use.
Go to a Local Hobby Shop, Michaels, or Hobby Lobby, ALL kinds of cool sharp objects to hurt yourself with there! Er.. I mean cut styrene with. Don't limit yourself to model tools, look in all the sections. Woodworking, pottery, scrapbooking, etc. Neverknow what you might find.