What you suggest above is called "Perpetual Motion", aka "Over-Unity". This goes against the laws of physics--you will always lose energy due to friction, drag, heat, etc, so you will not be able to keep it going. So that part is downright impossible, sorry to say.
The first thing I'd get for a small 120v Tesla coil is the high voltage transformer. What size are you hoping for? The height of your coil will help determine the size of transformer you'll need.
I'll walk you through this step by step if you like, but the parts you'll need are a transformer, a capacitor bank, a spark gap, a primary coil, a secondary coil, and a topload. This is assuming you're going for a Spark Gap Tesla Coil (SGTC) rather than a solid-state. Solid-state Tesla Coils (SSTCs) are generally MUCH more complex and not recommended for beginners.
I'll be asking for your input throughout the process. Tesla Coils can be quite finicky, so we will need to work this out the best we can together.
Regards,
Matt