Well it looks like most of your questions have been answered pretty well, but being an EE I feel like it's my duty to at least post something in this topic.
I have some leds in my Longshot that I run off of a 9v battery. It's not the best battery to use, but it is usually easier because it provides the voltage levels you need without being too big to fit in a gun.
As far as the switch, this is something I like to do. Get a two position switch, should be easy to find at radioshak or somewhere similar. You will be looking for a switch labeled as SPDT (single pole double throw) What you do is have the first position hooked up to be on at all times and the other you can run through a second button so that the lights will only be on while you are holding down the button. Make sure when you buy the button is is a "Normally open" type so that the circuit is open until the button is pressed. This will give you the option of constant light or a quick blinding flash for ambushes. This is a little difficult to explain by words, so if you want I can draw up the circuit.
In the serial vs parallel debate I am going to go to the side of parallel wiring. The "proper" way to build this circuit would be to have a power supply that would be about 6-7v higher than what you need for you load (the LEDs). Then you would build a circuit with 3 parallel loops, each with it's own resistor and it's own led. In an application like nerf gun lighting, efficiency isn't as big of a concern and components failing isn't going to be catastrophic, so if you wanted to have all the LEDs share a resistor it probably wont be a huge deal. But putting them in series will make it significantly more difficult to get the correct resistance values, so just go parallel.
Also keep in mind that white light LEDs are built to function drawing ~20mA of current, which is what that calculator angel linked is doing for you. You can put more juice into them, and they will be brighter for a while, but it is at the cost of severely lessened lifetime as well as greatly reduced battery drain. So don't be tempted to go low on your resistor just because it looks a tad bit brighter. Unless you feel like replacing LEDs every couple weeks.
One question for you, are you planning on soldering these circuits or using some alternate method?
TL;DR: most of your questions have already been answered but I just felt the need to use my degree in some manner.
Edited by Longbow, 30 August 2009 - 09:30 PM.