My daughter's boyfriend needs an old bike fixed up. Too bad you don't live closer to him. He bought an old bike off craigslist sight unseen and guess what he got? Some 80s bike with flippers to change the speed on the bike LOL I told my daughter I used to have one of those and it was a 10 or 12 speed. I loved it but why would he pay so much for an antique? Rummage sales usually have low cost bikes because people want to get rid of them and they work! Her boyfriend can't ride this one because it needs repair.
If the frame is sound the rest of it can be fixed at a push. Cables are relatively easy, you just need a new cable and the inclination to feed it through everything. If the frame is bent you might as well chuck it in the trash because the chances are you'll never get it quite right, and you really don't want the frame letting you own.
If the wheel rims are badly worn they can be replaced but it's a bit fiddly to do. Wheels are essentially consumable - the brake pads will slowly wear the metal of the rims. Newer rims have indicators to warn you they are getting thin (like the frame, you really don't want the wheel to come apart while you're moving!) but for older wheels you'll have to feel them with your fingers to try and gauge whether the sides are worn.
Most other stuff on a bike is fixable, it's just a question of how much time and money you want to spend on parts. If it's an old bike with a freewheel instead of a cassette it can be trickier to find the parts when they need to be replaced, and with the increasing push toward 10-speed and 11-speed systems it gets progressively harder to find things like chains for the older 7-speed and 8-speed systems.
A book I bought a few years ago, titled "Zinn and the art of mountain bike maintenance" is well worth a read. It covers just about every part of maintaining a mountain bike. The first time I built a wheel from component parts I had my truing stand set up, the wheel parts on hand, and the book propped open in the appropriate place to guide me through it. That first attempt at building a wheel resulted in a really nice wheel. I still have it, even though I broke the bike I used it with years ago and about all it has done for years is gather dust.
