i would build it as a pro touring type of car. either stroked small block or stroked big block. sitting low and mean with 17-18" rims set up to hit the corners. keep the a/c and all. would be a cool *** car.
+2!
As much as I love drag cars, I really like cars that can do everything well. My dad's always been a straight line focus, without attention to brakes or suspension.
Make a budget first, then make a list of all/any parts you will need. For the first go around, try to build with budget parts.... suspension/ you don't need the ultimate tube suspension right away, some bushing, sway bars, and steering box with go a loooonnnggg way.
Engine/ Most times it's pretty expensive to build a motor from scratch, of course most of use would love a beloved 340, but they're getting hard to come by. Possibly find a 5.9L out of a truck, and convert it to carb? There's lots of cheap good motors on craigslist and ebay, and make sure you do a compression check first on all cylinders if possible. And also try to check the crank thrust if you can with a dial indicator to see if the bearings are still in decent shape.
Paint Body/ This is the part that usually takes the longest. Strip the body down to bare medal by hand, it's alot less work than tearing apart the whole car and having it blasted, which usually ends up with warped panels anyway. A dent puller, hammer and dolly, bondo, and some blocks will make it a "quicker" one month body project if at all possible. Then you could just run it in primer until you have enough money, and a location to do the paint. 90% of a nice paint job is the prep work, the actual painting is simple and can be done in a weekend.
Good luck man, love those cars 8)