For a Tesla coil you will need massive amounts of small (20g) wire, and a winding mechanism to get the coil neat and straight - Quite an undertaking. All it is a glorified transformer. On the other hand, A van de graaf is a metal ball attached to a long tube for to run a belt of rubber. A brush assembly is attached to the lower housing and another to the top ball. The idea is to 'brush' electrons off of the lower metal housing and send it up to the top metal ball via that rubber belt. You would be better off buying a complete generator. They are not expensive.
Tesla invented alternating current AC, which allows electricity to flow for thousands of miles of wire. Every home in world w elec has AC, unless have own generator, DC, Edison's preferred source of elec, DC, needs power source nearby. Tesla refused Nobel Prize, cause wud have 2 share w 'mere inventor' Edison. Example of DC: car battery; flashlight battery; own generator. All elec co's send AC 'out'. AC/DC get it. 2 forms of elec power. Tesla saw himself as 'discoverer of principles'. Disliked Edison passionately, cause Edison took credit 4 Tesla discoveries, more than just radio.
How do Tesla coils work?
a Tesla coil is simply a high voltage transformer capable of producing 1,000,000 volts, it primary consist of a primary transformer to power the Tesla coil witch is the secondary transformer a PVC tube with a couple hundred windings of copper wire. i hope i answer you question if i did not you now have a different idea of a Tesla coil.
The power from the mains enters the first LC circuit and resonates between the capacitor and the primary coil (which is typically 10 to 20 turns of thick wire). The voltage in the circuit increases greatly in the secondary coil (which is typically between 100 to several thousand turns). This secondary coil, along with the toroid and the ground form another LC circuit building capacity until an arc is formed.