How to chose the right voltage and coil(s) for coilgun?
I think you need to understand at what point the magnetic field needs to begin collapsing in order to prevent the projectile decelerating and hence losing built-up momentum. I have done a simulation of a 44 mm long 10 mm radius air cored solenoid to enable to concepts to be more clearly seen. I have made it this shape just for my convenience in answering and I have no-idea if this is shape is useful in the real thing. Below is a picture of the flux density inside and outside the solenoid along with the gradient of said flux density: -

 

Regard the blue trace - flux density (for a given current) rises as you approach either side of the solenoid. At 22 mm either side of the centre line is the aperture of the solenoid. As you enter the aperture it can be seen that the flux density rises to an almost constant value - by this I mean that if the solenoid were really quite long then maximum flux density would be constant for most of the central length of the solenoid. This is important to realize because when the gradient of flux density is zero there can be no mechanical force exerted (such as in the centre).

So, it's important to look at the gradient (red line). If the projectile enters from the right, the force that accelerates it is maximum as it enters the solenoid (for a typically small projectile). After it has entered it will still accelerate but to a lesser degree until it reaches the solenoid centre. At this point it will start to decelerate (not wanted).

The upshot here is that you need to start turning the mag field off somewhere between the projectile entering and reaching dead centre. This is impossible to do instantaneously because of the solenoid's inductance but given that you can measure the inductance at least you can begin to calculate when to start the process (noting that any magnetic field remaining as the projectile passes dead centre is going to slow it down). 

Here are a few extra formula and observations that might help.

The force exerted by a solenoid on a ferromagnetic object is: -

Force = \$\dfrac{(N.I)^2\mu_0.A}{2g^2}\$

Where N is number of turns, A is cross sectional area of solenoid, I is the applied currents, g is the gap from the end of the solenoid to the object and \$\mu_0\$ is \$4\pi\times 10^{-7}\$.

Also, for a solenoid, inductance can be calculated thus: -

Inductance = \$\dfrac{\mu_0.N^2.A}{l}\$

Where \$\mu_0\$, N and A are as before and \$l\$ is length of solenoid.

So, making the inductance bigger makes the force bigger and, to keep turns as low as possible you want the length of the solenoid to be a short as possible.

However, with a bigger inductance it takes longer for the current to ramp up to maximum and this will reduce the effectiveness of a coil-gun due to not being able to accelerate the bullet to sufficient speed.