1995 Corolla Rough Idle

Hmmm the muffler? I guess that might be it... because there's some amount of rust on the underside of the car. It's been garaged for the last year, but sat outside for the 14 years before that. What would the spark plug wires have to do with the rough idle? The exhaust definitely sounds deeper... I was told by a friend maybe the EGR valve needs cleaned? it sounds better when the engine gets warmed up.

That is a HUGE piece of information that would have been helpful here. There are a number of things that could likely go bad or component lifespans have been greatly shortened.

As for the plug wires and distributor cap and rotor - those are part of a good comprehensive tune-up for this generation of Corolla. If the plug wires are in anyway damaged, they will cause mis-fires that would result in poor idling. Given its mileage, age, and how long it sat outside - I would do a complete tuneup - basically start from a clean slate. Otherwise you'd be chasing your tail trying to diagnose some of these symptoms.

Tune up for this generation of Corolla is pretty straightforward. Other than fluid exchanges (coolant, motor oil, transaxle fluid - automatic, gear oil - manual, powersteering fluid, brake fluid (master clutch fluid - manual). Normal wear items - tires (tire rotations), brakes, rotors, drums, struts, suspension, axles, bushings, etc. - all as needed)

Cap and rotor, plug wires, sparkplugs, air filter, oil filter, v-belts, timing belt, belt tensioner, waterpump - all as needed. Some things you can do separately that can have a decent impact with little cost to you (other than time) - throttle body cleaning, clean out EGR ports, check for vacuum leaks, visually inspect for obvious signs of leaks, damage.

In your case, those exhaust donuts in the exhaust system can dry out and leak over time. Really common on the 8th gen Corollas (1998-2002). On the 7th gen - they had issues with cracked exhaust manifolds. Check for any discolored marks in the exhaust system - those indicate an exhaust leak. Sometimes you can't even see the crack/leak until you remove the part - as heat will move the system around a bit.

As for the Matrix XRS - yeah, that was one hell of a car. Almost guaranteed that would have outlasted my Corolla (currently 180K miles) - Matrix XRS ran flawlessly. Only issues we've had with the Matrix was a bad upstream O2 sensor (heater element shorted out). Ran the nuts off that car as well - never babied it. Got a good price on it, as it was a company car originally - poorly maintained, they used it to haul dogs around - still have the OEM oil filter?! Engine was slightly sludged over, dipstick had a discoloration band right where the oil level ran too. Immediately ran some synthetic diesel motor oil in it + some Rislone/MMO, couple of short drain intervals - UOA testing showed it to be good as new.

I too was surprised to see so many transaxle issues with the 6-speed. So much so, that I picked up a U240E automatic transaxle from a Celica GT-S to swap in. But I've towed with the Matrix, shifted a touch before redline, a few times even accidentally banging off the limiter. Taught the little lady how to drive stick in the car (not a good first timer's car for learning standard shift - but she got the hang of it). No grinding, no noise, etc. But I religiously changed the gear oil every 15K miles with Redline MT-90 exclusively.

Unfortunately, got totalled out this year (July) - freshly paid off to boot. Picked up a 2009 Matrix XRS to replace it - completely different beast. That 2ZZ-GE engine in the 2003 Matrix XRS was a marvel of engineering. Who knows - maybe I dodged the transaxle "ticking time bomb" that some people started calling the C-60 transaxle. But in my experience - the car and drivetrain were pretty much bulletproof.