Pretty much the first thing everybody wants is more power. Now, I maintain that the first thing to worry about is the handling and that a stock engine is fine to start, but it is true that as you develop the chassis, more power is good.
As you might guess, there isn't much you can do in Stock, but here are a few things you might consider:
There is some arguement as to which basic engine is best for autocrossing. I do not have exhaustive data, but it seems to me that the Stinger Stage III long block probably offers the best basis for the engine, the biggest drawback being cost. I don't have enough data on turbos to comment, and of the remaining stock engines, there is no advantage to the smaller engines and no weight penalty for the late motors, so some variant of the 164c.i. units should be your first choice. Bear in mind that the 140, though it has more peak power, also has a peakier torque curve, so any advantage in stock form is pretty small. An *automatic* spec 140 might be a really good choice, as it can be mated to a standard trans, and offers a very good torque curve indeed. Speaking of automatics, don't dismiss one out of hand, they have the advantage that you can probably run the whole course in low. A looser (higher stall) torque convertor would be helpful. If you wish to run a turbo, pay special attention to the ignition and carburetor.
Here then are some modifications that should work pretty well on any Corvair engine, and are SCCA legal. Look here for more info on how Corvairs can be modified under SCCA rules.
Putting one of the late engines into any early car is pretty simple, just use the shrouding that goes with the car the engine is going into. 140's can be a bit tricky in an early, as you will probably not be able to also fit the spare tire in the engine compartment, and the exhaust on the driver's side will be a tight squeeze. You'll also need to trim a set of early model side shrouds for the secondary carbs and the left lower shroud will need trimming (or use a '64 A/C piece) for the twelve plate oil cooler, or you'll need to swap in a folded fin cooler. The clutch stuff will swap, but you need to use all matching clutch pieces (flywheel, disc, cover, throwout bearing and pivot ball). For the engine mount, use a '64 engine bracket and mount (the earlier setup will not clear a harmonic balancer although a cast pulley will fit) along with the rear engine sheet metal. If you want to put a late (balancer equipped) engine into a '60 or an FC, do all of the above but instead of the '64 car engine bracket and mount use the '64 - '65 FC bracket and the standard '60 mount.
It is legal to change ignition systems on stock class, as long as you use the stock distributor. Street Prepared cars may use any ignition system, triggered any way you like. There are several different systems which can be used. IMHO, a stock system is just barely adequate for street use, however the advance curve is crucial to good performance and Chevrolet went to a lot of trouble designing a good curve for each engine. Do not just put any old distributor in your car, start with the proper one. There is a table in the Corsa Tech Guide of ID numbers showing which distributor goes in which engine along with details of what parts belong in it. Here are a few of the alternatives:
See also my other pages on ignition:
I do not recommend running an engine without an air filter. However, the stock air filter assembly is quite restrictive at high RPM, so you may want to simply remove it during events. If you do, put some sort of screens over the carb inlets to keep leaves and other big junk out of the engine.
A better alternative is make the air filter work better, either the stock unit or some kind of aftermarket filters. Depending on your Corvair and engine, there are a few different styles that will both flow more air and still keep dirt out of your engine. Go here for more info.
Corvair engines from '64 up all have a Positive Crankcase Ventilation (PCV) system, they all use the same 1/2" vent tube, which is .19 square inches. If you need more venting for a high rpm or turbo engine, you could make a larger vent:
5/8" = .3 sq in
3/4" = .44 sq in.
1" = .78 sq in.
Carbs are a big enough topic that I've set up this entire page on the topic. Take a look before you get rid of the Rochesters.
Heads are really the key to making power, and again a big enough topic that I've set up a separate page to cover them.
The stock fan is at its best up to about 4,000 RPM. Above that, the tip speed gets high enough that the fan starts just creating turbulence, rather than pumping more air. Further, the belt has difficulty staying on at high speed, especially when the engine speed is rising and falling rapidly.
So, there are a couple of things which can help:
Obviously, any of the last three will reduce the air flow to the engine somewhat at idle and cruise. Keep an eye on your temp gauges (you have added an accurate temp gauge of some kind to your engine, right?) to avoid melting down the engine. There were some rather detailed discussions on Virtual Vairs and FastVair, I've gathered some of the posts here.
So you want headers on your Corvair? I've run headers on the coupe for about ten years now, and here's what I've learned:
For most people, headers on a Corvair are not too good. The best answer is to put slant tubes in the head, so you can have a real flange to bolt up to, and then they won't leak. The heater problems still exist, however. As Ken Rolt pointed out, a good exhaust will help all by itself. The "extractor" style exhaust will be a little better if you're staying with manifolds, since the gases cool somewhat before they hit the muffler, although I'm not too fond of the glasspacks they usually come with.
If you look in the Corsa Tech Guide, there is a set of plans for making clamps that fit over the down tubes and hold the headers tight against the flanges. If you ran these, AND mount the exhaust well, AND run good turbo mufflers, it would probably last a long time.
That said, I STRONGLY disagree with many folks about headers in general. The reason most header equipped cars are noisy is that they are usually bolted to noisy mufflers, like glasspacks, and they are often poorly installed, so they leak. On a normal (front engine) car with a full exhaust and quiet mufflers, most people can't tell (I have headers on the Road Runner). To the point that somebody didn't believe the car was header equipped until I opened the hood. Even the Corvair is reasonably quiet when the headers are sealed up. Good headers will last several years, but they are obviously not as durable as 1/4" thick cast iron manifolds. The further north you go, the shorter their lifespan. Down here it's about five to ten years, depending on how much snow the car sees.