If this is for 1 or 2 snakes, use the sprayer but if for a large system, use a garden hose and a filter.
I purchased 2 misting kits from Barrs. They included about 15 feet of hose, 4 "T" connections, 3 misting jets and a hose adapter. If you can run a standard garden hose to this system, that's the easiest but you will have to use an in-line filter of some type. I haven't gone that far yet!
Anyway, route the misting jets the way you want them in the cage. Buy some wire guides, small plastic for attaching wire to the wall, and run the hose through it. This will keep it from coming loose in the cage. The adapter that Barr's gives you, basically a hose type end, will connect to a digital lawn timer you can get at Lowe's or Home Depot. About $50. I think the one at home depot allows you to water 6 times per day. You can program it to go off as little as 1 minute each time for up to 6 times each day. That's the most I've ever seen cycle wise. Connect the "in" line of the timer to a hose or a garden sprayer. Obviously the hose comes from the spigot but the sprayer is about $20, again at Home Depot or such. It's a pump type sprayer and make sure you get one with a pressure release valve. This helps when opening it to refill it. MAKE SURE YOU OIL THE PLUNGER AS DIRECTED IN THE INSTRUCTIONS! If you have to do allot, get a large sprayer. Best bet though is a filter and a hose from the spigot for allot of misting.
Hose: Just run a garden hose to some type of filter. If you are in a decent area, the folks at the store should be able to help you out filter wise. Run the hose from the filter to the lawn timer and you're all set. Keep a SMALL amount of pressure on the hose, play with it to see what works best, and the timer will do the rest. If you want more control, buy multiple timers and purchase the "Y" adapters for running multiple hoses and run multiple misting systems from one filter and spigot.
Pump: Run the hose from the pump to an adapter that will fit the size of the hose onto the timer. Basically the adapter is nothing more than a hose end repair piece. Plastic with screws so you can push the hose onto the adapter, then clemp it down so it doesn't come off. The adapter screws right onto the timer. You have to pump the sprayer as often as it needs but I've gone a week without having to pump before. That is only for 1 misting jet though.
The instructions that come with the misting jets form Barrs will tell you how to keep them clean and not clogged. Trust me, it's simpler than it sounds.
DZ