I actually have an old Giant Iguana that I think was bought around 92. That is what I used to get back into riding 4 or so years ago and still ride it regularly. Mine is a 3 X 7 Shimano Altus setup and I've had no problems finding replacement parts and pretty inexpensively.
When I first got it out of storage, I found the rear wheel rim bent and purchased a used replacement wheel from my local bike shop. I think he charged me 15 bucks. Both trigger shifters were gummed up and I found replacements on amazon. I think those were less than 20 for the pair. The originals were a combo brake lever/shifter and the replacement was just the shifter so I took a dremel to the old levers to cut off the shifter part and have both mounted on the bars. There are plenty of tires available for the 26 X 1.75 rims from knobbies to slicks so you can run whatever tires you want. I have Schwalbe Marathons on mine. I also cleaned and repacked the bearings on both wheels and the fork bearings.
I think that is all I did just to get it in good working order initially. After riding it regularly for a while, I noticed a grinding sound in the bottom bracket so got a replacement for that, which was I think less than 20 bucks. The two larger ring gears were pretty worn so I found a replacement crankset on amazon that was around $40 and figured since I was doing that, I'd get a chain and cassette as well, neither was very expensive.
All that stuff was easy to find. Search for parts using Shimano Altus in the search.
I ride this bike in the early mornings and sometimes in the winter when the weather is lousy so I've also added fenders. Right now I'm putting 50-60 miles a week on it and it's quite reliable.