What Jason said, basically.
You don't really need a new crank. I would put one in there anyway if it were me, cause you'll be in there anyway and I don't trust brass bushings in anything kitted.
Get a Leo Vince HM pipe if you can find one, otherwise get a Simonini.
The stock variator blows, get a Malossi or Polini and a set of weights off ebay (I bought a set of 3ea 3g-9g rollers for like $10). They don't need to be Polini or anything special like that.
Get a toothed belt, either Malossi or a Gates AX39; they last longer. Also make sure you install the rear spring that comes with the variator.
Make sure you cut the crank and drill the intake to 13mm, and of course match the transfers with the kit. Also get the Malossi filter or the treats clone, not the Polini one.
New gearing isn't strictly necessary for what you want, but it might make your motor love longer depending on what kind of terrain you're riding. That can easily be done later, though, so leave it off for now. If your motor is always screaming and you're WOT all the time it might be worth getting.
A well built motor with these components will last a very long time. My Grande has more than 7000 miles on it since I kitted it (64cc Malossi) and all is well with the motor. The key to a very reliable vespa moped is the electrical system. For some reason they seem to have more than their share of problems in this area if you dont set them up right.
Make sure you get real Piaggio points, not off-brand aftermarket. I have snapped the crank follower off the aftermarket ones.
Hardwire it if possible.
The generator system itself is solid.
If possible, switch to a Kinetic CDI setup. It'll bolt into place where your points equipment normally goes. You'll need the flywheel and CDI box too, and a voltage regulator. It'll give you nice bright 12v lighting, super easy starting, and reliable, maintenance-free ignition.