go look on ebay for the tokico suspension kit. That is a good place to start. Then you will want to get some bigger sway bars. Go for the Suspension Techniques set. Look on yahoo shopping, and search for "280zx sway bars" and you should find something. This will improve the handling dramatically. Then you will want to get some new tires and wheels. Get at least 16" wheels because there are more tire options. There are alot of ways to go with wheels, you will have to do some research on that. I would save HP upgrades as the last thing. Make sure the car is handling well first and in sound mechanical order.
The first thing for the handeling is the tires. What class are you going to race in? I race in F prepared with 15x7 wheels with goodyear 23x15x9 tires with the sofest compound available(r250). I have raced the car with street tires and slicks with the same set up as far as suspension and stuff. The difference was almost 18 seconds. That is very dramatic but I went from some of the stickest tires made to some of the worst tires made (Cooper Cobras). That gives an idea of the difference tires make. If you are giong to go street prepared then I would use the Hoosier As04 225/45/15 as the smallest option. If you use fender flares then go with 275/45/16s. If you run coilovers then you can go to 245/45/16s with out fender flares. I do not have flares on my car (yet) so my tires go past the fenders but they do not rub because they are only 22.5 inches tall (they equil 264/36/15) the 275/45/16 will rub so you must use flares with those tires. For f prepared with flares then use 16x10 wheels with 10x23.5x16 in the r250 compound, with out flares use the tires and wheel size I use.
The suspension is the next thing. If you can afford it, get coilovers and use tokico illuminas as the shocks. If you have the money get shochs ones such as ADR from Ground Control. If you do not go with coil overs then the springs to use are the Arizona Zcar heavy duty. They are the stiffest (180 front 200 rear) I could find, I have used them for a year. They would be good for the 225 45 15 Hoosiers. With the larger options (such as the tires I use) go for the coil overs with 400 inch pound springs, the Azcar spring are not enough.
Before you try to make more power GET A LIMITED SLIP!!!! If you can not put the power to the ground then power is useless. The inside wheel will spin around corners no mater what type of tire and suspension you have even with the stock power plant if you do not have a LIMITED SLIP. Go for 3:90 or lower gearing.
I have been very sucessful with my car this year against some very nice f prepared cars such as 911s and other well perpared zcars. I probably make less power than all the other cars in my class but I beat them often because I have good tires and a better suspension. I do not think my car has more than 170 hp at the crank. I have an L28 block with an E31 head. Every thing is stock in the engine even the cam and the carbs are the stock SUs. In autoxing power is the last thing to give you a winning margine. After you have perfected the cars suspansion and drive train and driven it for a while then worry about the power.
To simlify things a bit. If you have never autocrossed before then go and race the car as it is right now to see if you like it. Do not compare yourself to the people that have raced for a long time. If you do like it then start to modify the car. You are on the right track. Researching the options is the most important thing you can do before you spend any money because some of the things I listed can be very expensive. Ask other racer (experienced ones) what they did and get advice from them as well. Good luck