I agree with Priest start out slow. 1st thing you need is a place to nurture seeds and veg.
And it seems like your grandparents are really nice people and see your needs for the meds which I fully understand needing the meds. And because of your GP's I'd use the shed instead of the closet, everything will go fine in the closet for the next 12 wks, but then comes wk 6 of flower and you haven't gotten the cash together for odor control, I hope you see where I'm goin'. If you can get temps controlled in the shed start there it will keep the stench out of the house.
As far as floro lights, IMO tube fixtures are better for seeds, clones and veg than compact. If I were you I'd start in the shed build a box against the brick wall (which is a house wall I assume) and build it on the floor. This will give you the coolest area in the shed. Build it big enough to house a 6 tube 4 ft T-5 fixture. But to start install a 4 tube T-8 shop light fixture > $20 with 3 6500k & 1 3000k bulb $4 each this will take you through seeds and veg. Then hopefully you can afford a T-5 or small HPS lamp for flower.
I've been thinking about starting a thread on growing MJ with minimal labor and $$ invested. Here's an overview:
You need 4 things to grow anything. Water, Light, Food, and Air.
Water - Here is where hydro is cool because it fills 2 rolls, both water and growing medium. But start up costs take it out of consideration for a cheap grow. You can put together a great bubble system for less than $50 but you will need ph & tds meters & an assortment of chems just to start (don't even try if you can't afford these). Now the H2O itself, if your tap water is halfway descent - ph 7.6 or less and tds of less than 200 you can make it through a soil grow and not kill anything.
Medium - not part of the basic 4, but very important. In your position I 'd stick to soil, buy a bag of of Fox Farms Ocean and Forest, or any other quality potting soil. Do not buy Miracle Grow or any other soil with frets in it, not saying it won't work, but as a beginner its better to stay away from it and its not good for seedlings (no ferts for youngin's). If I could recommend the best medium I'd go for a modified hempy which is a whole lecture by itself.
Food - Better known as nutes. Here you could blow your whole budget again, but there is no need to. Use Osmocote Plus or just standard Osmocote (the plus has micro-nutes) This is a controled release fert and it works just fine for mj, and then for a flower boost use some Miracle Grow Bloom Boost, you'll only need 1/2 strength 2 maybe 3 feedings during flower. And see if you can get a little Super Thrive. Grandma may have all this already.
Study up on a SCROG grow, it has the best yield for low wattage grows.