I'm guessing this one is not chromoly. I remember I had a Sprint, then got Schwinn's next step up (can't remember the model offhand, but probably similar to the OP's bike) when I outgrew the Sprint. Then I got a 1984 Schwinn Le Tour Luxe with lugged chromoly frame and all alloy components. The Le Tour Luxe was a huge improvement over those other bikes in *every* respect, and I think if I was going to sink substantial money and effort into an old frame, I would want at least that level of quality. It was a $300 bike when I got it.
I still have the Le Tour Luxe by the way, and it works as well as it ever did (but aesthetically challenged by now). I'll be selling it this year - I just have other bikes that I prefer.
On the other hand, if I had a Schwinn World and a limited amount of money to buy something better, I wouldn't hesitate to spend a few bucks here and there for cables, brake pads, or whatever it needed to be reliable and safe. To OP: keep your eyes and ears open. You just might find a 1980s lugged steel chromoly bike at a fair price. If I was in the market, I would even spend $100 - 150 on one in good condition. That would leave plenty left for tuning up and buying whatever accessories you need.