It might not be fair to compare your car to your friend's. First, an 84 TA is not that light of a car, and the rear suspension isn't great either. Right off the bat you've got a couple of disadvantages. If you're going to plan on pushing 12 seconds with a car like that you're going to want a decent hook and some gears to motivate the thing along with a posi rear. Further, 12 seconds on a factory, 23-year-old trans is probably also a shady bet. If it were my car, here's how I'd do it as I got the money, piece by piece.
Make sure you're working with an 8.5 inch rear with a 3.73 posi (or similar). You'll want trac bars and a little wider than stock tire for traction.
Replace your U-Joints with upgraded units. You don't have to spend a ton just get something a little stronger than stock.
Inspect your transmission. If you think its in good shape then put a 50 dollar shift kit in it, replace the fluid and put an adjustable vacuum modulator in it to dial it in how you like. My guess is you'll probably want a rebuild.
Build a motor using a post 1987 350 block with the one-piece rear main. I'd spring for a stroker crank with a few extra dollars. Flat tappet cam is fine, something like a XE284 comps would be fine. Toss a minimum 2500 stall behind it (3000 preferred). Heads will be your biggest expense- if you don't mind replacing gaskets a few times you can experiment with some home-ported heads, but my guess is you'll end up wanting something aftermarket. Lots of guys like the vortecs due to the price/performance benefit, but plan on a new-style intake which may upset the amount of savings you get out of the vortecs if you already have an old-style intake that you like. I'd keep compression with iron around 9.5:1 or close. Plan on running high-test.