Sounds ambitious! But a couple of thoughts:

LEDs are quite ready for Prime Time - yet. They are getting better but the initial cost for a decent one (not those 14 watt, 225-bulb panels) is so exorbitant. Shop lights, or an array of 6000K CFL bulbs will not consume much more electricity and are a lot cheaper.

I would use reflectors for everything, or at line the walls with Mylar or paint them white. For the HID, you definitely want an overhead reflector.

IMO, root veggies such as potatoes, just like corn, do not yield enough produce for the space they take up, unless you have unlimited room. And unlike tomatoes, lettuce, peppers, eggplant, etc., you get one harvest.

Any particular reason for only growing heirlooms? There are several varieties of tomatoes that are ideal for indoor growing. I can understand if you want to save seeds, but if you plan on cuttings, seed saving would not be a concern.

(24'x 16'x 7')

I take it you mean inches and not feet?!

Good luck,

Mike

Remember to consider cost to grow vs cost to buy them. compare prices to both the box stores as well as specialty grocers. I can't grow yukon gold for $4 and get a 5lb yield, thus I won't grow them and at the box store they taste fine for my pallet. Now toms are another thing altogether.
If you're going to grow without a reflector, make sure to buy a bulb that can be placed vertically. And also be very careful with regards to looking at the light. They'll pretty much be at eye level and can really burn up the retina.
And finally, regarding lettuces and continually picking; be sure to look into the variety and find what works. I was going to do that but after a month or two, the leaves started having a bitter flavor.Later, in some thread here, it was suggested that happens to lettuce with age. I was growing grand rapids.

LED's have been used for quite some time now and work very well IF they are used in a complimentary manner. Packing 1000 lights together as close as possible and then hanging that light above a plant is not as useful as spreading that 1000 lights out over broader area at a much closer distance. See linked news article here.
I find the cost of food purchased also has the hidden cost of what was done to that food by the producer in order to get it to me. Potato's can be purchased rather inexpensively but are doused with chemicals that I would rather get away from at any cost. Unlike an outdoor garden that requires preserving to extend your food supply into the winter I can grow a much smaller amount continuously with out the need to preserve as much food for as long.
Light placement has been my latest concern. Placing a light above a horizontal growing surface is an inefficient use of space. I can see 20 head of lettuce being grown vertically in less square footage as 4 head grown horizontally. When planing how to use the space in my basement this becomes very important. The Use of artificial lighting as efficiently as possible is also a major concern. Providing light to as many plants as possible per light is an absolute requirement. Hydroponics has proven to be extremely flexible for plant placement. I am still working on making my vertical growing stands for leafy vegetables and the vine plants are not yet tall enough to give visuals for what I am wanting the garden to look like but I am excited for the opportunity to share my ideas with like minded people.
Thanks for the responses so far
Brad