for your hydroponic system, I would build my own custom-made, custom fitted aeroponic system. There might be easier hydro-systems but why not start with the system with the fastest grow potential and learn the in's and out's right off the bat. Why invest in an Ebb and Flow or other system and work your way up to aero? waste of time and money IMO for very limited differences in ease of use.
Your budget is more than adequate to achieve what you are looking for.
You want to exhaust (air-cool) your lights using a different fan that the one used for exhaust.
also- have you a plan for moving A LOT of water in and out of your grow area?
anyway - here is a little something i wrote up regarding choosing a grow area/room which may help...
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The Grow Room or Closet
Before we can begin growing, we have to make some decisions regarding where to grow and what equipment to use. That's what this section is all about. But before we start making a shopping list and knocking out walls, let's decide where we're going to grow.
The ideal grow room should have the following qualities:
Clean - you don't want to give a lot of dust, mold, mildew, insects, or other unpleasant things easy access to your plants.
Climate controlled - you want an area that you can have some control over the temperature and humidity.
Secure - you don't want your garden to be accidentally or easily discovered. Some advice I heard was there should be no less than two locks between the outside and your plants. We'll also need to make sure we can control any odor emanating from the plants.
Easy Access to Water Source - this one is often overlooked. You dont want to be running a garden hose through your bedroom or carrying heavy buckets of water up and down many flights of stairs. Not having easy access to fresh water can take the joy out of gardening.
Easy Access to Fresh Air - somehow, someway, fresh air must be able to enter the growing area, which infers a way to exhaust hot, stale and often very smelly air will be necessary.
Easy Access to Enough Electrical Sockets - provided it is convenient, heavy-duty power cords can be used to bring electricity to the garden. Often, it is necessary to add circuits to accommodate the electrical requirements.
Light-Tight - Finally, you'll want to be able to make your grow space light-tight. That means no light should be able to enter or leave the grow area. You want to keep light from exiting to prevent it from attracting unwanted attention. And no light should enter as to not disturb the plants photoperiod.
Fire/Water Proof- don't want anything easily ignitable in there. Also, a way to catch leaking water can save you much more than just money; especially if you have downstairs neighbors.
I'm sure a few areas sprung to mind. Closets, basements, attics and spare rooms all have their pros and cons. You can also purchase a grow tent. Building or modifying a cabinet is also a very popular option.
It is best to accurately sketch out the area you plan to use and draw in where all the components go.