Rotating Mass
These mods, as well as the weight reduction (redux) can be sprinkled in with the breathing mods at will. They are put on separate pages for several reasons, mainly because I felt like it. If you plan ahead, you can avoid doing a task twice. For example, if you are replacing the timing belt and/or head gasket, it would be a good time for a UDP (see below). If you are putting in a new clutch and flywheel, might as well put in a limited slip as well.
Torque takes two factors into consideration: distance (from center) and weight. For an engine, the more something weighs, or the larger the diameter, the more work has to be done on it by the engine. Like I said before, your engine makes X amount of horsepower, because there is an explosion inside the cylinder that forces the piston down and makes the crankshaft turn. There's a lot that can happen to that power from that point to the pavement, and anything that is getting turned by the engine is robbing torque that could be making your car move.
Underdrive Pulley - UDP for short. On one end of the crankshaft, there will be a pulley or series of pulleys that are used to drive accessories like the power steering pump, the air conditioning compressor, the alternator and sometimes a water pump, air pump oil pump, fuel pump, etc. On the Neon, one pulley is used for accessories, where one belt drives the alternator, and the other drives the a/c and power steering. Aftermarket manufacturers make replacement pulleys that are both smaller in diameter and lighter than the stock pulley. Additionally, many have models that drive only the alternator, meaning the engine no longer has to work at powering the a/c and power steering. Simply removing the ac/ps belt frees up 4 HP on the SOHC engine. Add the effects of an UDP and you have freed up 10 HP or more! What you are really doing is freeing up torque, so it's rpm dependent. Nonetheless, this is an excellent mod to slip in wherever you like on your list. If you decide against those nasty accessories, you can pull them out for some weight savings. The downside is that you will lose some traction (located over the wheels, roughly) and will be shifting the weight balance even more to the driver's side (affects handling and traction).
Lightweight Flywheel - Same concept as the UDP. The stock one is a big hunk of steel. The aftermarket ones are strong, lightweight aluminum. Do this with a clutch replacement. For Neons with modular clutches, you don't have much choice in this, as it comes as a unit. This is pricey. And tearing into your tranny might not be within your mechanical abilities just yet. Don't worry, the time will come. And you'll thank yourself later for not taking it to a repair shop.
Wheels - Same concept as the UDP and lightweight flywheel. Let me say that again for those looking at 20" rims on e-bay. It's the same concept as the UDP and lightweight flywheel! A larger and/or heavier wheel robs torque. Period. So why are the tuner boys rollin' on dubs? Because they get a free sticker with a set of four, that's why. A taller wheel can help with stability on tight turns. Then again, so can a stiffer-sidewall tire. If you must have the bling-bling wheels, at least invest in lightweight drag wheels for the track. If you are doing autocross or lots of tight, high-speed turns, try going up 1 or 2 inches in size at the most from stock, and keep them as light and narrow as your ego can handle. Acceleration is important during autocross as well, and some of us even like it on a daily basis! Due to the high cost of good wheels and slicks, this is another mod that will probably wait for later. Plus you'll want to do some research on which tire size is best for you, and you'll want to know more about your gear ratios before you start down that road.
Inside the block - There are things you can do inside, but these things will be taken care of on their own as time goes on. For example, using lighter weight pistons and rods will reduce losses. Putting in a lighter weight crankshaft may help some, but he cost vs. gains is phenomenally ridiculous.