We bought a cheap, second-hand bike (Schwinn Ranger, 24 inch wheels) for my wife (she's on the short side, and this size seems to work well). She won't let me buy a more expensive bike because she doesn't cycle much - only on weekend rides with me and our son. I want to make sure its not unsafe though - so here are a list of things wrong with it:
1. Brakes - weren't working very well, and both calipers were not striking the rim equally. This was the first thing I worked on, and the brakes work pretty okay now.
2. Right shifter is broken. There is no tension on the rear derailleur cable, so the chain has settled into the smallest cog and works fine there. I haven't been able to figure out a way to make it permanently stay in one of the middle cogs - that would be nicer since there would be less cross chaining when she changes the front gear.
3. Rear wheel is not true.
4. Just yesterday, the bike made a clicking sound - I don't know where it's coming from yet. All spokes are okay, and it doesn't seem to be coming from the drivetrain - I flipped the bike and ran through all the gears to see if I could reproduce the sound. Need to experiment a bit more before I can start looking at a solution.
So of the problems above, which one should I start working on first (apart from brakes)? W.r.t safety, which is the most important? I don't have many tools either, so I will buy and fix - but don't want to make too many expensive fixes (simply because it isn't worth it - at that point, I would rather try convincing her to get a new bike instead).