Yea sorry man that all seems too complicated for a beginner and small time operation like mine at least.
I have an 80 dollar budget give or take I just need to know what specific brand and type of soil and type of light fixture
First off, you can get a lot of stuff at home depot, but if your is anything like mine (i live in las vegas, so we have "big city" selection) you dont want to buy your HID (HPS or MH) lamp there. The only ones I saw when I went were ones made for driveways and garages and shit, and they didnt come with ballast. I mean you could use it but you'd have to wire it yourself. But this was like 5-6 years ago so IDK.
I just wanted to make a point about spending a lot of money. Those who say that cheap is a bad idea have a point. You should at the very very least, buy a good light. And a good CHEAP light is gonna cost $150 for like a good 200watt CFL grow light (not the weaker ones you get at home depot. YOu could go that route but youd need more lights). Hell you could get a 250 watt HPS for $150, then grow like two plants in a Scrog system and get bumper crop for the effort.
Also, you really should get some type of fan or venting system - about $30-$50
And you should get some decent nutes. Im not even gonna try and tell you what kind you should buy cause thatll start another fight, but it'll cost about $20
Pots- You can get grow bags for .10 a peice but pots cost anywhere from .99-how ever much you wanna spend. I suppose you could buy a solid gold pot..
Soil/medium- This depends on how many plant and what type of system your growing in. Soil generally cost more. You could spend a lot of money on soil. Id suggest if your a broke foo like myself, that you use rockwool, and make yourself a simple ebb and flow (flood and drain) table. If you make it from scratch itll cost you about $30-$50 to do it right assuming you have drill or a friend you could borrow one from.
Finally, youll probably use tap water at first, but depending how your local tap water is, youll want to purchase R/O water, how ever you do that. I have to lug around the 5 gal bottles..
SO...Yes, i have started gardens with $5 and for the most part theyre right, you reap what you sow. So this is about as cheap as Id waste my time with at this point in my life