I'd suggest selling that 340 and 4 speed to the resto crowd. You can put a 6.4 Hemi/six speed pullout combo in your car for less than you'll build the 340, and put the sale money towards that. This gives you almost 500HP with dead nuts reliability and no oil leaks.

Once the drivetrain is sorted, I'd look at suspension. I'll make this one statement, shocks are VERY important. My opinion is unless your willing to put a clip on the car, work with what you got. Hotchkis has good stuff. The bolt on front suspension systems available basically move your cars geometry from the late '60's to late '70's.
If your willing to change the front, couple of places sell the rails that mount C6/C7 corvette cradles (rear IRS/transaxle too!). It's a cheap way to get good geometry, suspension components, and brakes in one swing.

Your going to want the widest tire you can fit, preferably a square set up (same size up front as in back). This helps balance the car. The weight is biased to the front (even more under braking), and those front tires are what lead on turn in, so wider the better. This may be tough utilizing the factory suspension, so flares may be necessary (note of caution, adding positive offset will change the scrub radius). Upgraded brakes will be dependent on what size tire you put on it (both width and diameter) and intended use. Autocross cars really don't need big brakes. Track cars can benefit from them. Huge brakes with huge brake torque are pretty useless if you can exceed the mechanical grip of the tire.

Weight reduction is probably the biggest bang for your buck. The car is more responsive and requires less brake and tire than a similar heavier car.

Aero on these old cars is important. They generate so much lift. My initial goal would be to decrease the lift, more so than adding downforce. That is basically the same thing, but if your generating 200 lbs. of front lift stock, and can reduce that by 150 lbs., you did increase downforce, but in my mind your still just reducing lift. I call it downforce when I've overrun the lift numbers. An air dam and splitter to keep air from under the car will go a long way, and cheap to make. This little add will be your most significant "reduced lift" mod you will make. Try to avoid a huge spoiler on the back until you can ascertain the aero balance of the car. Adding a ton of rear downforce on a car that is already wanting to lift the front makes a very unstable, scary drive, as your just compounding the front lift issue.

Only other advice is have fun. Your not in competition with anyone but yourself. When you get it on track, only make changes when you can string together a series of consistent lap times, then, only one change at a time and preferably A-B-A testing.