Yes, vinegar would be good to remove the rust spots and then touch in with some paint. Rather than clean and grease the chain perhaps a new chain? All you’ll need is a chain cutter. In fact most of work it needs is very simple and straightforward so could done by you. New cables inners and outers, bartape. Tyres and inner tubes might need replacing. The only thing you might need the bike shop for is if the spokes are loose and need truing. YouTube is your friend when doing these jobs.
Good luck.