What type of capacitor will bring the highest current?

It depends somewhat on the circuit, but energy is .5 C V^2.  In general, increasing energy increases the current.

The one that holds the largest charge!

What the heck are you talking about?

You need to be a lot more specific. As is, this doesn't make any sense.

Any capacitor would be capable of very high currents, limited only by the internal resistance.

"run a capacitor through a coil" huh? how do you do that?

For storing energy increasing the voltage is much more productive, but capacitors have a maximum reliable voltage. For storing current increasing voltage or capacity gives equal results, but in most circuits there are other considerations, so telling us your application details may be helpful. How many turns of what gauge wire are you thinking for your coil, and what is the coil diameter and length?  Neil

I'm going to make some assumption about what i think you are talking about. What I'm imagining is that you have a coil/solenoid that you want to give a momentary charge to to move the solenoid or make a brief electromagnet with the capacitor. I'm also assuming that you're using some diode/MOSFET/relay connection to let the capacitor discharge into the coil after it is charged.
The capacitor equation is Q(charge) = C*V. If you know your battery/charge setup you can find out how much charge will be in the capacitor by multiplying your  capacitance by your voltage. Current is just moving charge, so obviously, a larger capacitor will have more charge. This mean a bigger capacitor will give you a larger discharge current. I hope that helps.