I'm having a hard time deciding what to make for my first MC piece... I'm praticularly interested in 3D curved flat shapes and carved detail, but I suspect these may not be good choices for a newbie who is torch-firing the pieces.  Any recommendations for what techniques are easiest for beginners (but not too cookie-cutter, although USING a cookie cutter would be OK...)

I highly recommend taking a class. The benefits are enormous! A class can give you hints and tips that you may not know yet. You also have access to a knowledgeable person to alert you to potential hazards (like do not let your clay come in contact with aluminum), as well as much needed technical and some design information. Plus you get to meet other people who share your enthusiasm! If you want to start out on your own, check out websites (like this one) and others for beginning projects and read! There are tons of books out there on the subject. Good luck and have fun with it!

I second the class recommendation, if it's possible.  I took a quick intro class at a community college nearby and absolutely loved it.  Great intro into the material with helpful tips on how to achieve different results.  I honestly wouldn't disuade you from trying a 3d curved piece either, it'll help you get the feel for the material and how it behaves when fired.  (some pieces will bend a bit, etc)