Pre-Staging
You need to have some sort of baseline to start from. Even if your car is the "sporty" model, it still has some things purposely inadequate. The manufacturers do this for several reasons. First, they don't want to sell you a car, they want to sell the car to a lot of people. Even Joe Yuppie thinks better of himself if his car says, "GT," or "Sport," or whatever else on the side. But Joe Yuppie probably also wants a sunroof, power windows, air conditioning, leather interior and a wood-trimmed dash. Oh yeah, and 18 inch chrome wheels, ABS and four wheel disc brakes. That's not to say that the sporty models are slow, they are just a lot slower than their potential. Second, manufacturers have their own aftermarket. Toyota has TRD, Chrysler has Mopar, etc. So they can build the "sports car for everyone," design better performance parts at the same time, guarantee them to fit, sell them at a heck of a profit, and add the costs to the purchase price if you like. Finally, numbers and names sell. The names we all know as "true performance" cars like Mustang, Corvette, etc. will always sell, even if they really aren't that quick. For example: with my lowly SOHC Neon (a couple of bolt-ons and some weight reduction), I stayed nose to nose with a mid-90's Corvette from 0 to just over 90 (he backed off). How? His 250 or so HP against my 135ish HP? Well, he had an automatic tranny (much more power loss through the drivetrain), weighed over 1,000 lbs more than me empty, and it was just my 150 lbs. against the driver and his passenger, both weighing in in the 250+ range. My power-to-weight ratio was practically identical to his. But, if you were out to buy a sporty car... and 250 HP does sound might impressive in the commercials... I think you see what I mean. Great. Now, let's get your car ready to modify.
Tools
Before you even get started, you need some tools. Don't try to convince yourself that you need to take it to a mechanic for everything, or that you are just no good with mechanical stuff. The fact hat you have the drive to turn a sport-compact car into a race car means you can and should do more than the average guy/gal on the street. At the very least:
Socket sets, metric and SAE, don't skip any sizes. Specifically, 8, 10, 13, 15, 18 and 22mm will be the most frequently used
Deep well socket sets, ditto
Set of open/box end wrenches, ditto
Socket extensions, at least a 3" and a 6"
Torx bit set
Nut driver
Either a screwdriver set or one of those interchangeable tip screwdrivers
Digital multimeter
Vice grips/channel locks
Large breaker bar with a 1/2" drive
Drive adapters (1/2" to 1/4", for example)
Oil filter wrench
Small crowbar
Hydraulic jack
Set of jackstands
Set of wheel chocks
Fuse puller (or you could use the vice grips...)
Torque wrenches, ft-lbs and in-lbs
Brass punch
If you have the means to get power tools, go for it. Jobs will go much faster. Otherwise, just pick stuff up as you need it. No sense in dropping a ton of cash on tools right off the bat. When you need a 22 mm deep well socket to take off your struts, get the whole set, and plan in advance.
Engine Mounts
It seems like a lot of money to shell out for something that doesn't increase your HP. But factory motor mounts are notoriously weak. They are this way so it's quieter inside the car, and more commuters, grocery-getters, grandmas, etc. will buy the car, not just the performance nut like you and me. Your choices range from barely better than stock, to pretty much solid mounts. The stiffer the mounts, the more vibration inside the car. But you also get better shifting ability (for manual transmissions) and better traction. That adds up to better times at the track. There are 3 mounts for automatic trannies - front, left and right. Manual trannies also have a bobble strut in the rear.
Budget - you can inject windshield urethane into the gaps on the stock motor mounts. Ideally, you should remove the mounts from the car. Total cost will be probably under $10. Total time to remove and install all mounts (one at a time) will be under 2 hours, plus a day or two (each) for curing time.
Best - Deyeme Racing sells completely new front and side mounts in "flex" and "firm" versions. Howell Automotive sells a solid front mount and bobble strut, Modern Performance sells the solid Booger bobble strut. Total cost will be anywhere from $225 to $250. Total time to install, including removing the old ones, under 2 hours.
Best for the Money - Deyeme firm side mounts, AFX solid front mount, and the solid Booger bobble strut.
Other mount options - Energy Suspension, Prothane, and Rex make inserts that fit in your stock mounts. If your stock mounts are torn, DO NOT use inserts. It will actually be cheaper to replace them with aftermarket mounts than new ones from the dealer. Mopar makes a font mount and bobble strut. The front mount is barely stiffer than the stock one, and tears almost as quickly. The bobble strut is also barely stiffer than stock, and is actually the stock part on 1995 Neons. Blackdog Motorsports has recently added a fully solid aluminum side mount package. I will update as more user reviews come in, but they do look promising.
Fuel
Use the fuel that is recommended by the manufacturer. For example: the SOHC Neon is supposed to run on 87 octane fuel. The computer "brain," or PCM (Powertrain Control Module) is actually programmed this way. If you put higher octane fuel in there, it burns faster, which means the peak pressure in the cylinder is happening before the optimum rod angle, which means you are losing torque. The end result is poorer performance and, usually, worse gas mileage. Octane boosters and fuel additives are a waste of your money for nearly all computer controlled, fuel injected vehicles. The stock PCM's can only retard the ignition timing. They would need to be able to advance the timing to take advantage of higher octane gas. If you reprogram your PCM, or buy an aftermarket one, and the ignition timing is advanced, then use the higher octane fuels recommended by the PCM manufacturer. If you increase your compression ratio, you have to increase the octane.
Oil
If you don't have a huge number of miles on you car (less than 60,000 or so), and you don't have any noticeable oil leaks, make the switch to synthetic oil. Mobil 1 and Amsoil seem to be the choice for most Neon owners. 5W-30 should cover you year-round in just about any part of the continental U. S. Use a quality filter (Mobil 1, K&N, etc.) as well. Sure, you might be paying for a brand name sometimes, but that extra 3 or 5 dollars every 3,000-5,000 miles is cheap insurance. For Neons, you can use the larger diameter Dodge Viper oil filter if you like. It may sit a little lower, so if you've lowered your car, check ground clearance and avoid speed bumps. If you do have high miles and/or an oil leak, you may not want to make the switch. Regular oils can gum up and fill in little voids and cracks that form over time. If you put in synthetic oil, those deposits will become soluble again, and you have lost the "plug" that's been keeping your engine from leaking. The best time to do the switch is in the first 5,000 to 10,000 miles. Fram makes a cool drain plug adapter that make changing your oil even easier.
Spark Plugs
Unlike oil, the more expensive spark plugs are usually just gimmicks. If your engine is so overloaded that a different brand of spark plug gives you more than 1 HP, you've got serious problems. The FTC charged Splitfire, Inc. with false advertising, for example, because they claimed more power, better fuel economy, etc. It was simply a lie to sell parts. Neons should stay with the cheap Champion spark plugs as recommended by the manufacturer. You can get a slight gain in HP by gapping them a little bigger. 0.040" is a safe gap. Anything beyond 0.045", and you might have too much heat in the cylinder when the fuel starts burning - not where you want to be with a stock car.
Spark Plug Wires
Just like spark plugs, there are so many gimmicks on the market, and they all cost more money. The factory and factory replacement wires should be fine. The Mopar plug wires will give you a little more piece of mind, and you'll have a clearer spark signal. But that shouldn't make any difference until you are making quite a few more HP. Read the article at http://www.magnecor.com/magnecor1/overview.htm and you'll get a better feel for what wires actually do. Python sized wires and wires that come in 145 cool colors are best left to the car show crowd. If you want true performance, buy what you need, and don't waste your money on gimmicks. An improperly made wire can and will damage your engine.
Body Kits, Paint Jobs, Graphics, and Stickers
I am all for each person making their car unique and individual. Just try to keep a few things in mind. First, body kits usually add weight to your vehicle. That slows you down. Carbon fiber and fiberglass hoods take weight off your front wheels. That reduces your traction. And NO "aero kit" manufacturer has proven (i.e. wind tunnel testing) that their kits improve the vehicle aerodynamics. It's your car in the end though. Second, a glass smooth paint job just might help your drag coefficient. But if you are spending $1200 on a custom paint job as a performance enhancer, you are wasting your money. Third, Graphics and stickers do not make you go faster. The reason real drag racers have them on their car is because 1) those manufacturers have contingency programs (they give you a few bucks if you win a race and have their sticker) and 2) they actually have those products in their car! NOS seat covers and an APC windshield banner are for people who have no idea what performance really is, or for people actually sponsored by NOS (that's right, it's a company, not a substitute term for "nitrous oxide") or APC.
Wings and Spoilers
Muscle car owners of old discovered a few things as their speeds got faster and faster at the race track. The shape of their car was similar to a wing (more surface area on top than underneath), and there was a lot of turbulence underneath the car. This meant that the car would try to lift off the ground as the speed increased. The problem with that is loss of traction. Traction helps the car go forward, as well as stay in a straight line. By putting a wing, or flow spoiler, on the back of the car (over the drive wheels), they could help counter these effects. As speed increased, downforce on the wing would help keep traction to the rear wheels. Enter today's sport-compact cars. Most are front-wheel drive. Most sit lower to the ground than the old muscle cars did, so there's less turbulence. So what reason is there to put a wing on the back? That's right, NONE! I've heard all the arguments about high speed cornering or rear end traction on the track. Bull. A wing made for high speed cornering looks completely different, go to a circle track sometime and watch the mini's. And if you are reaching speeds in the 1/4mile that would require a wing for rear end stability, I salute you. I would also assume your suspension is top-notch, you have a baby-smooth undercarriage, and your front airdam is the best money can buy. That's why you need that wing, so your back end doesn't get squirrelly at 195+ mph.