Sorry.... this is long...
Legal to run and competitve are two different questions.
To be legal to run, the car needs to be in good mechanical condition. You will need a seat belt that works. Many autocross inspectors require a dual throttle return spring on non-stock vehicles. Clean everything out of the car before you go to tech inspection -- don't forget to remove floormats. Remove hubcaps if you have them. Depending on the tire and wheel combination air them up to 30-35lbs. Torque your lug nuts. Bring or borrow a helmet.
To be competitive, you will need good body roll control (springs, shocks, sway bar combo), the shelby drop for front suspension negative camber control, and a good competition alignment (1/2 to 1 degree negative camber, 2 1/2 to 3 degree's positive caster, about 1/16 inch toe-in). Wheels and tires are also critical. Run the widest, stickiest tires allowed in your class with appropriately sized wheels. In addition, you will need front disc brakes (at least) with an aggressive pad compound. If you haven't done so yet, change to an appropriate (drum/drum, disc/drum) dual master cylinder. It could save your life (and others) on the street or on the track. I also use stainless steel brake hoses to improve braking effectiveness and brake pedal feel.
A Monte-Carlo bar, export brace (with firewall reinforcement), sub-frame connectors, and welded-inm roll bar will help with structural rigidity. At minimum, I'd do a properly installed export brace and Monte-Carlo bar. (again to be competitive - not required just to have fun).
Horsepower and weight reduction come after you get the handling right. A good chassis with moderate power will beat an ill-handling powerhouse all day long. | 
