That is an excellent start!
I have to ask why you are not using a linear power supply to charge up the caps. It seems like an easy way to accomplish a 200 volt source.
Well mainly because the power supply i have is a kit I built a few years ago, and only goes up to 12 volts. But the main reason is i want to be able to finish the coil gun and know that i made it from “scratch.”
That, and the fact that i need to drag my presentation out to a full 40 minutes, so I’d rather go through the formulas, and show how the boost converter works rather then just say “well this power supply charges the caps”. But yes, using a power supply would be MUCH easier, but just ask my mentor, “easy” is not in my vocabulary 
Railguns are slightly different from coilguns. In a coilgun, coils of wire around the barrel are used to pull the projectile down the barrel. A railgun uses two rails which the projectile slides down. In a railgun current passes down one rail, through the projectile and back down the other rail. Railguns have the advantage that they accelerate the projectile evenly down the entire length of the barrel. To do this, a coilgun would require multiple stages.
But with each stage comes more complications. I think i will make a multi stage and a single stage. A multistage requires 1 capacitor bank PER coil. They also require an IR detector system to trigger the next set of coils(unless you can figure out the excact timeing, which is almsot impossible). But despite which kind i build, first i need to get the boost converter working, once thats working everything else is easy to make. It’ll also give me a chance to use one of those PIC microcontrollers i have
That is an excellent start!
I have to ask why you are not using a linear power supply to charge up the caps. It seems like an easy way to accomplish a 200 volt source.
Would a voltage multiplier work??? Abeit, I have no idea if that type of design would applicable since it’s a high voltage and low current device.
The simplest thing to do in this situation would be to get a line operated high voltage transformer with a secondary winding of 300 volts center tap. (I am guessing right now at the numbers) In a full wave rectifier, you might be able to get 200 volts DC to charge the caps or to fire the energizing coil. Transformer cost in the $50 + range new, total supply less than $100 (fuse, line cord, diodes and trerminal strips). This is a common transformer in tube type equipment and might be found in a junk TV or radio or at a Hamfest.
What Phil is trying to make is what some people call a “whistler supply”. It uses a low voltage DC power source like a bank of batteries, running an oscilator to produce an AC voltage capable of driving a low voltage primary winding on a transformer. The secondary winding is a high voltage winding much the same as the linear supply described above. The difference is the transformer core. At 60 Hz you need a lot of iron to couple from the primary to secondary windings. At 1.5 kHz or above, the core becomes more efficient and so the need for a heavy iron core is diminished. MOst often these supplies are actually running at much higher frequencies like 10-15 kHz. When they operate, the supply can be heard as whistling. This type of supply is comon in a camera photo flash unit when first turned on. Since you need an oscillator and high power driver (sometimes the same device) this is a much more complex device. The upside is the transformer is a fraction of the weight of a line operated supply. However, 200 volts is still 200 volts regardless of how you get there.
High voltage batteries were plentiful at one time when portable radios were tube operated. Finding them now is next to impossible.
The boost converter is a fun project in its own right. Learning to build switch-mode power converters is worth the time spent. I’m a little biased here; switch-mode power converters were one of my earliest projects (after audio amplifiers) a couple dozen years ago when I was getting started in electronics.
However, if you just want to charge capacitors, a simple charging circuit using a 115VAC line cord, a full-wave rectifier, a couple of resistors (one in the 50 to 100 Ohm range in series with each capacitor for current limiting, and another in the 100,000 to 200,000 Ohm range across each capacitor to bleed off the charge when it’s not in use) and a suitably rated, insulated switch for each capacitor you want to charge would do the job nicely, if you can make the coil gun work with about 170 Volts dc on each capacitor.
If you need higher voltage, or if you need to adjust the voltage to control the gun, or if you just want the fun of building a switch-mode circuit, then go on ahead with the boost converter. 
Also, if you are planning on a multi-stage gun with each stage fed from its own capacitor, you will probably want to have a separate voltage measurement circuit for each capacitor so you can tell when they are charged.
Insulate all the high voltage connection points well with electrician’s tape or heat shrink tubing. If you plan to demonstrate the device (and why else would you build it?) then it’s a good idea to enclose everything in a non-conducting project box after you get it working. And, yeah, keep one hand in your pocket while the circuit is live. 
Stay safe and have fun. 