Step 2: Words of Wisdom
The IGBTs: or "bricks", as we like to call them. They should be good for 600V (not a concern, I've never seen a brick rated under that before), at least 200A (I use 400A modules to be, safe), and more importantly, need to be fast. This is where you need to check the datasheet - IGBTs have an inherently long turn-off delay. For 65 kHz operation, rise time + turn-on delay + turn-off delay + fall time should be under 2 uS.
Bricks come in several types: single-transistor, dual transistor, 6-pack, and some rarer types such as chopper modules. Single-transistor modules are prevalent for 1200V and larger IGBTs, and have the highest thermal ratings and are the most difficult to mount. Duals (half-bridge modules) are the much easier to mount and can dissipate less. They are most common for 600V modules. 6-packs are used for 3-phase inverters, require no external power connections, and have the lowest thermal ratings.
Use what you see fit; this tutorial uses half-bridge modules.
The tank capacitor: is very very important. It handles tremendous amounts of reactive power at very high frequencies. It is absolutely essential that this part be selected appropriately. It must be a high-quality polypropylene or mica capacitor. I use giant snubber capacitors made by Eurofarad; alternatively, a series/parallel array of smaller capacitors (such as the Tesla coiler's beloved CDE942 series) should work. The ultimate capacitor, of course, is a water or conduction-cooled unit made by Celem, but such caps will run you about $150 for a 2 uF unit. You want enough capacitance to resonate with your work coil at no more than 70 kHz.