If you had to do a basic demonstration, what techniques would you use?
Big ones. A nikyo where you only move your hands about two inches may be what you prefer to practice (although personally, I don't), but no-one will see you doing anything.
As others have noted, a progress from "softer" techniques to more advanced techniques, speed, and style may be a good idea. Don't force uke into a breakfall on the first shiho nage you demonstrate - unless, of course, that is how you practice this technique all the time.
We usually (i.e., every few years, when there is a reason for a demo) start the same way we start our training (sans warm-up), by bowing and doing a few rolling exercises. What seems to work well is to show the attack first without nage moving away, it makes understanding the movement much easier.
We also tend to combine lots of techniques where the average spectator has the feeling of knowing why something has happened (such as ai hanmi katate dori - ikkyo, yokomen uchi - shiho nage, or chudan tsuki - kokyu nage, short form) with techniques that look much stranger, such as a nikkyo against grapping a jo. (May look easy to a trained eye, but I've heard a number of people wondering what just happened.) Also, spectacular falls like koshi nage or other breakfalls I would place into the later stages.
Would you incorporate weapons into your demo?
Unless time is really short: Definitely. Weapons are part of our training, so if we wish to demonstrate our training, we should include weapons. Although I must admit we don't use them as much in training as I'd like and for demos, it's sometimes reasonable to use weapons hardly ever seen in our dojo, such a short baton or baseball bat to get one possible reason for a yokomen strike across.
Personally, I wouldn't use weapons that look too real. Some people use blunt metal knifes for demos, and while it looks much more spectacular than standard wooden tanto, I'm not sure I want to give the impression we practice with live blades.
Just my 0.02€.