If you plan to ride the bike regularly, the first priority should be to get the brakes in perfect working order (because failure can get you injured or killed) and a close second is the shifting and drive chain. It would probably be easiest to replace brake and shifter cables all at once. Likely it is time for a new chain, but rust per se isn't as bad as it looks. Rather, it indicates you haven't been keeping the chain lubricated. Chains are cheap, so make a fresh start. The ghost shifting should disappear with new cables and adjustment (assuming it isn't complete junk). If the new chain skips, it means you need to replace the cassette. I wouldn't paint it.

Learn (and make mistakes) on this bike, and then when you reward yourself with a new one, you will be ahead of the curve on maintenance. Since it has sentimental value, you probably will at least want to keep it as a backup.