[NOT A TA]

If you're seriously gonna go for it with a 12,000.00 budget I'd suggest you keep it simple. Build a car like my Firebird but lighter and with more power. Mine cost about 10-11 thou several years back.

Tires!
The widest stickiest tires you can get away with! If you can mini tub the rear within budget do it. I run 315 35 17's and 275 40 17's without tubs but the 315 rears won't fit on Camaro's without mini tubbing. I run Yokohama AO 32's but there's other tires out there also. Light weight 17" wheels without blowing the budget.

Weight!
Trunk mount the battery in a cheap box to the inside (pass side if they run clockwise there). Replace the front bumper with a cheap fiberglass one for the "race"(I have one on my 74 Camaro and it only weighs a couple lbs)and use light weight mounts for it instead of the shocks. The weight of the battery, bumper, and bumper mounts is cantilevered in front of the front wheels and makes a huge difference. Ditch the inner fenderwells(for the race) and air cond. system if it has them now. The lightweight front bumper isn't a safe idea on the street so keep the orig to put back on for daily driving. Install a factory front spoiler and keep the rear one to add downforce. The rear Camaro one is actually better than the TA one I use on my Firebird.

Suspension
Hotchkis kit (orig designed for 71 Camaro) includes springs sways tie rod adjusters etc and get the offset upper control arm shafts from them. They also have Bilsteins to match if you want or there's some adjustable ones available to aid with tuning. Global west upper and lower control arm Del-A-Lum bushings unless your budget allows buying the tubular arms with the bushings already in them. Subframe connectors(weld in if you're confident with a welder) Solid or Poly body mounts.

By purchasing a suspension kit you eliminate the guesswork of what works well with what. You also eliminate the learning/tuning suspension problems. just get the front end aligned to the specs they give you and you're done. Suspension engineers have already done all the development and testing! It won't stick like a racecar but should give you enough cornering capability be good enough in the corners to use the power in the straights to win.

Engine/trans/rear
I don't think you need to blow the budget on a 6 speed for the "race", you really only use a couple gears on most tracks so if you gear the rear accordingly then a 3 or 4 speed is all ya need for this kind of race and budget. I use a 2.72 or a 2.41 10 bolt posi rear for road tracks with a 3 speed auto so I can hit 150 MPH in the straights without killing the motor. It's not drag racing from a dead stop so you won't need those 3.73's and 4.10 kind of gears. Sounds like you'll have the BBC so you'll have plenty of horsepower even naturally aspirated with no power adders.

Brakes
The 2nd gen cars have pretty good spindles and brakes so for your "race" just get a good set of semi metallic pads and shoes (bedded in properly on freshly machined seasoned rotors and drums) and make sure the system is optimized with a new master, hardlines, and the flexibles. Use the Ford heavy Duty DOT3 fluid which holds up as well as "race" fluids at much less $. Install cooling ducts to the front rotors if you can but it's not necessary for your "race".

If you haven't been around that track with a really good driver to teach you the line then sign up with N.A.S.A. or another group for the HPDE events and then practice that line. Seat time in your car is going to be important because you're going to run against an experienced guy that knows the line and is familiar with his cars limits already.
GOOD LUCK!!!