For our purposes, nearly all HID lights are sold with a ballast that you plug into the wall. From the ballast is a cord to the light. There are also ballasts attached to the light, but since the ballast can represent a major portion of your heat build up, it is best not to have it in with the plants. Outside the fridge somewhere would be even better. No wiring.

The problem with HID's is not how to get light, but how to get rid of the heat. Also is stealth an issue? Kind of a dumb question considering your sherrif, but you will need to grow a non smelly weed, or use some kind of odor control, preferably a carbon filter. I and most people are not going to tell you how to build your set up from scratch. You'll need to research this forum and perhaps other web sites. Try to figure things (especially the basics) out for yourself, then post specific questions. Look at other peoples grows and grow logs. There is even a grow log section of this forum.

You are correct about sucking in air from the bottom. Heat rises so you'll want your intake near the floor to get cool air. I know you said you're on a tight budget, but Zandor, a former mod said if you go cheap you'll grow cheap, and that hit the nail on the head. Try to get a digital ballast for just a little more money. It has many advantages, including paying for itself within a year as opposed to a traditional ballast.