I'm clueless about transistors & ICs, Can someone help me with a charging circuit?

Hi, I'm new here, just registered yesterday, and wondering if someone can help me build my coil gun.
I forgot all about coil gun fun until I several youtube videos about them and I started dreaming about building one, previously I stopped building them due to lack of spare cash for capacitors and stuff. Now I have a steady job, have a few bucks to spare each month and looking for a new hobby.

I have some background with electronics, I used to study electronics in college but had to give it up since i just don't get digital circuits & IC's. I also have a hard time understanding inductance in relation to capacitance & resistance cause my induction.

There's two basic coil guns I built from before, my first was a converted photo flash circuit that I just attached a NO push button to and my own coil made from 22 AWG magnet wire, it shot BBs about 15 feet.
my second was an improved photo flash coil gun system that I used more a capacitors- 330V @ approx 3300 uF. i used a bigger coil made from 14 AWG wire from home depot- it's not magnet wire. I think it was 15 turns wide and 3 turns high. It could shoot a finishing nail about 35 feet at about 35 fps. But the battery would get extremely hot- as if you're shorting it every time the gun is charged. after 2 shots in rapid succession the plastic on the case would bubble & blister, and 3rd shot it's a dead battery. Same for the charging photoflash IC- stuff melted and broke often. I determined I needed a new charging circuit but clueless how to build one. I've tried using schematics I found on google or copying the photoflahs circuits to no avail, I honestly have no idea what I'm doing when it comes to using any kind of transistor or IC.

Can someone please help me and explain it in terms an idiot can understand?

In the 3 years since my last build I got 12- 400 volt 3900 uF capacitors, originally intended for a rail gun build (that never panned out- got sidetracked with the injector design). They're big blue caps the size of a 20 oz beer can. Radial type connectors.
I have a large supply of 14 AWG wire, 22, 26 & 32 AWG magnet wire.
I'd love to have a charge circuit that can be adjustable to different output voltages between 200 to 400 volts, so I can tinker with the voltages and find one that works best with the coil, capacitance and bullet.

I understand I need a big diode to protect the charging circuit, any idea how big I need? in volts & amps?
I'm planning to pull electricity from the wall. Batteries are expensive, mains power is cheap. It's 120V AC 60 Hz.