Good grief, guys--how can a simple question like "what is a good instructor's ski?" turn into a boasting match about your own personal skiing?
Sure, a very skilled skier (which does not, unfortunately, describe a lot of instructors in the first place) can ski pretty much any condition on pretty much any ski. But that makes no difference as far as the original question, does it?
The answer to the question is simple. The optimal ski for teaching is the exact same ski, in the same condition, as your student is on. That guarantees the most relevance and the most accessibility of your demos to the student's needs and capabilities. It's the same reason you don't demonstrate your best, highest-speed ripping carved turns to show a beginner how to make a basic, low-speed turn. Effective demos need to be something the skier could reasonably aspire to, and should look pretty much like what their turns will look like when they get it "right."
That said, "optimal" isn't always possible, or practical. As an instructor, you can't always know where your next lesson is going to take you, or what level skiers you will be working with. Even when you do know--which, as Uncle Louie has described well, you probably will as a new instructor--you cannot know exactly what skis your students will show up on. So a good practical instructor ski is a good, middle-of-the-road ski that is not going to be too far from what you expect your students to be on. I cringe when I see an instructor "teaching" a group of beginners while riding on a pair of monstrously wide, long, reverse camber planks. Skis like that bear very little resemblance to what your students will be on, and your demos--no matter how skillful you may be--will hardly look like their performance. It is very unprofessional.
On the other hand, I often go to lineup with a pair of full race-stock slalom skis. Ironically, at 165cm and with deep sidecut, they are not that different in size or shape from a typical beginner's rental ski. But I can also take a high-level skier into the race course, or work with intermediate skiers on anything. If I have to take them into bumps, crud, or powder, it's my problem, not my students' problem, and I can handle them there just fine. Yes, if I know that I'm going to ski with a particular level student, or in a particular type of terrain, or if I know in advance what skis my students will be on, I'll try to match their skis as closely as I can.
But that still doesn't really answer the original question here, does it? I have an extensive selection of skis to choose from, so I can pick with specific purpose. When I'm teaching, I still choose with my students' needs in mind, as much as possible. That is not the situation the original poster has described, however.
Jobsoccer, to answer your question, I would recommend that you own two pairs of skis. One should be basic beginners' learning skis, similar to what most of your students will likely be on. They are not expensive, and you may well be able to buy a used pair from the rental shop. These are your "work skis," and they're ideally suited for what you'll be doing most of the time. They'll get used a lot, and they'll get skied over, walked on, banged up, nicked, chipped and generally abused. The other pair should be a good, all-around, versatile ski that you enjoy skiing on yourself, that you will keep well-tuned and ski for pleasure, but that you probably won't teach on until you teach something other than beginner lessons. That ski will depend on where you ski, and where your personal preferences lie. If you spend a lot of time in the park, you may want a twin-tip. If you lean toward carving turns or racing, it should be a narrower, curvier, high-performance ski. If you ski a lot of powder and off-piste, you'll probably prefer something a little wider and softer. The further you go to any extreme, of course, the more specialized and limited the ski becomes. But this is a ski for you, not your students, and if you can only pick one, pick the one you want. Enjoy its strengths and live with its limitations until you can supplement it with another pair.
Once you've taught for a while, you'll be able to make your own informed decisions about equipment much better. Enjoy!